Journal of Algebra, ISSN 0021-8693, 01/2018, Volume 493, pp. 1 - 19

We investigate Hopf–Galois structures on a cyclic field extension of squarefree degree . By a result of Greither and Pareigis, each such Hopf–Galois structure...

Groups of squarefree order | Hopf–Galois structures | Field extensions | MATHEMATICS | ORDER | Hopf-Galois structures

Groups of squarefree order | Hopf–Galois structures | Field extensions | MATHEMATICS | ORDER | Hopf-Galois structures

Journal Article

2018

Hopf-Galois extensions were introduced by Chase and Sweedler [CS69] in 1969, motivated by the problem of formulating an analogue of Galois theory for...

Hopf-Galois structures | Field extensions | Groups of squarefree order

Hopf-Galois structures | Field extensions | Groups of squarefree order

Dissertation

Mathematical Logic Quarterly, ISSN 0942-5616, 1996, Volume 42, Issue 4, pp. 433 - 445

We extend the analysis of the decision problem for modules over a group ring Z[G] to the case when G is a cyclic group of squarefree order. We show that...

Pure injective module | Ideal class | Group ring | MATHEMATICS | group ring | MODULES | pure injective module | ideal class

Pure injective module | Ideal class | Group ring | MATHEMATICS | group ring | MODULES | pure injective module | ideal class

Journal Article

06/2019

Let $G$ be a group and write $\mbox{Perm}(G)$ for its symmetric group. Define $\mbox{Hol}(G)$ to be the holomorph of $G$, regarded as a subgroup of...

Mathematics - Group Theory

Mathematics - Group Theory

Journal Article

ACTA ARITHMETICA, ISSN 0065-1036, 1992, Volume 61, Issue 1, pp. 1 - 12

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 12/2016, Volume 44, Issue 4, pp. 875 - 904

Given a squarefree monomial ideal $$I \subseteq R =k[x_1,\ldots ,x_n]$$ I ⊆ R = k [ x 1 , … , x n ] , we show that $$\widehat{\alpha }(I)$$ α ^ ( I ) , the...

Secondary 13A02 | Primary 13F20 | Linear programming | Mathematics | Waldschmidt constant | Fractional chromatic number | Convex and Discrete Geometry | Graphs | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Monomial ideals | Symbolic powers | 14N05 | Combinatorics | Computer Science, general | Hypergraphs | Resurgence | RESURGENCES | X P-1 | MATHEMATICS | LINEAR-SUBSPACES | POINTS | Graph theory | Decomposition | Subspaces | Unions

Secondary 13A02 | Primary 13F20 | Linear programming | Mathematics | Waldschmidt constant | Fractional chromatic number | Convex and Discrete Geometry | Graphs | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Monomial ideals | Symbolic powers | 14N05 | Combinatorics | Computer Science, general | Hypergraphs | Resurgence | RESURGENCES | X P-1 | MATHEMATICS | LINEAR-SUBSPACES | POINTS | Graph theory | Decomposition | Subspaces | Unions

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 04/2017, Volume 40, Issue 2, pp. 697 - 706

For G a finite group and p a prime this paper proves two theorems under hypotheses that restrict the index of the subgroup generated by every p-element x in...

p-groups | Fusion | Finite groups | Supersolvable groups | MATHEMATICS | SUBGROUPS | Hypotheses | Subgroups

p-groups | Fusion | Finite groups | Supersolvable groups | MATHEMATICS | SUBGROUPS | Hypotheses | Subgroups

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 5/2009, Volume 29, Issue 3, pp. 389 - 404

In this paper, we prove that the arithmetical rank of a squarefree monomial ideal I is equal to the projective dimension of R/I in the following cases:...

Alexander duality | Convex and Discrete Geometry | Arithmetic degree | Almost complete intersection | Initial degree | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | Regularity | Arithmetical rank | MATHEMATICS | SET-THEORETIC INTERSECTIONS | Universities and colleges

Alexander duality | Convex and Discrete Geometry | Arithmetic degree | Almost complete intersection | Initial degree | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | Regularity | Arithmetical rank | MATHEMATICS | SET-THEORETIC INTERSECTIONS | Universities and colleges

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 3/2011, Volume 33, Issue 2, pp. 313 - 324

Let K be a field and S=K[x 1,…,x n ]. In 1982, Stanley defined what is now called the Stanley depth of an S-module M, denoted sdepth (M), and conjectured that...

Squarefree monomial ideal | Squarefree Veronese ideal | Interval partition | Convex and Discrete Geometry | Stanley depth | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | MATHEMATICS | DECOMPOSITIONS | INTERSECTION MONOMIAL IDEALS | CONJECTURE

Squarefree monomial ideal | Squarefree Veronese ideal | Interval partition | Convex and Discrete Geometry | Stanley depth | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | MATHEMATICS | DECOMPOSITIONS | INTERSECTION MONOMIAL IDEALS | CONJECTURE

Journal Article

Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 2/2011, Volume 54, Issue 1, pp. 77 - 89

Let A be a finite group acting fixed-point freely on a finite (solvable) group G. A longstanding conjecture is that if (vertical bar G vertical bar, vertical...

non-coprime action | automorphisms of solvable groups | Carter subgroup | fixed-point free action | MATHEMATICS | ORDER | FINITE-GROUPS | FREE AUTOMORPHISMS | Prime numbers | Mathematical analysis | Exponents | Fixed points (mathematics)

non-coprime action | automorphisms of solvable groups | Carter subgroup | fixed-point free action | MATHEMATICS | ORDER | FINITE-GROUPS | FREE AUTOMORPHISMS | Prime numbers | Mathematical analysis | Exponents | Fixed points (mathematics)

Journal Article

11.
Full Text
Betti numbers of strongly color-stable ideals and squarefree strongly color-stable ideals

Journal of Algebraic Combinatorics, ISSN 0925-9899, 5/2008, Volume 27, Issue 3, pp. 383 - 398

In this paper, we will show that the color-squarefree operation does not change the graded Betti numbers of strongly color-stable ideals. In addition, we will...

Graded Betti numbers | Colored algebraic shifting | Convex and Discrete Geometry | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | Balanced complexes | MATHEMATICS | GENERIC INITIAL IDEALS | balanced complexes | graded Betti numbers | COHEN-MACAULAY COMPLEXES | THEOREM | EXTERIOR ALGEBRAS | colored algebraic shifting | Information science | Statistics

Graded Betti numbers | Colored algebraic shifting | Convex and Discrete Geometry | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | Balanced complexes | MATHEMATICS | GENERIC INITIAL IDEALS | balanced complexes | graded Betti numbers | COHEN-MACAULAY COMPLEXES | THEOREM | EXTERIOR ALGEBRAS | colored algebraic shifting | Information science | Statistics

Journal Article

Bulletin of the London Mathematical Society, ISSN 0024-6093, 9/2003, Volume 35, Issue 5, pp. 635 - 644

The paper gives lists of all the primitive permutation groups of squarefree degree. All such groups are either solvable and act on a prime number of points, or...

MATHEMATICS | ORDER | REPRESENTATIONS | MAXIMAL-SUBGROUPS | FINITE CLASSICAL-GROUPS | ODD | CAYLEY-GRAPHS

MATHEMATICS | ORDER | REPRESENTATIONS | MAXIMAL-SUBGROUPS | FINITE CLASSICAL-GROUPS | ODD | CAYLEY-GRAPHS

Journal Article

Journal of Algebra, ISSN 0021-8693, 10/2012, Volume 367, pp. 105 - 119

Let and be the rings of monomial representations of finite groups and of odd order. We prove that the isomorphy implies the isomorphy of the respective...

Isomorphism problem | Representation rings | MATHEMATICS | FINITE-GROUP | SUBGROUP | ALGEBRA

Isomorphism problem | Representation rings | MATHEMATICS | FINITE-GROUP | SUBGROUP | ALGEBRA

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 9/2013, Volume 38, Issue 2, pp. 407 - 436

We construct an Eliahou–Kervaire-like minimal free resolution of the alternative polarization $\operatorname{\mathsf{b-pol}}(I)$ of a Borel fixed ideal I. It...

Borel fixed ideal | Discrete Morse theory | Convex and Discrete Geometry | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Eliahou–Kervaire resolution | Combinatorics | Computer Science, general | Squarefree strongly stable monomial ideal | Eliahou-Kervaire resolution | MATHEMATICS | Information science

Borel fixed ideal | Discrete Morse theory | Convex and Discrete Geometry | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Eliahou–Kervaire resolution | Combinatorics | Computer Science, general | Squarefree strongly stable monomial ideal | Eliahou-Kervaire resolution | MATHEMATICS | Information science

Journal Article

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 07/2017, Volume 125, pp. 80 - 94

For an integer , a graph is called a if its automorphism group contains a cyclic semiregular subgroup with orbits on the vertices. If is even, there exist...

Circulant | Cubic graph | Arc-transitive | SQUARE | SYMMETRIC GRAPHS | PERMUTATION-GROUPS | CLASSIFICATION | SUBGROUPS | DIGRAPHS | MATHEMATICS | ORDER | PRIME | SEMIREGULAR AUTOMORPHISMS

Circulant | Cubic graph | Arc-transitive | SQUARE | SYMMETRIC GRAPHS | PERMUTATION-GROUPS | CLASSIFICATION | SUBGROUPS | DIGRAPHS | MATHEMATICS | ORDER | PRIME | SEMIREGULAR AUTOMORPHISMS

Journal Article

Journal of Algebra, ISSN 0021-8693, 06/2013, Volume 384, pp. 110 - 134

In this paper, we give a sufficient condition for a set of polynomials to be a Gröbner basis with respect to a given term-order for the ideal that it...

Gröbner bases | Determinantal and pfaffian ideals | Liaison | RINGS | PFAFFIAN IDEALS | SYMMETRICAL MATRIX | DIVISOR CLASS GROUP | SCHUBERT POLYNOMIALS | MATHEMATICS | LADDER DETERMINANTAL VARIETIES | DECOMPOSITIONS | G-BILIAISON | Grobner bases | CANONICAL CLASS | GEOMETRY

Gröbner bases | Determinantal and pfaffian ideals | Liaison | RINGS | PFAFFIAN IDEALS | SYMMETRICAL MATRIX | DIVISOR CLASS GROUP | SCHUBERT POLYNOMIALS | MATHEMATICS | LADDER DETERMINANTAL VARIETIES | DECOMPOSITIONS | G-BILIAISON | Grobner bases | CANONICAL CLASS | GEOMETRY

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 3/2006, Volume 23, Issue 2, pp. 107 - 123

A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, Δlex—an...

Reverse lexicographic | Convex and Discrete Geometry | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Shifting | Computer Science, general | Combinatorics | MATHEMATICS | GRADED BETTI NUMBERS | GENERIC INITIAL IDEALS | MONOMIAL IDEALS | reverse lexicographic | shifting

Reverse lexicographic | Convex and Discrete Geometry | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Shifting | Computer Science, general | Combinatorics | MATHEMATICS | GRADED BETTI NUMBERS | GENERIC INITIAL IDEALS | MONOMIAL IDEALS | reverse lexicographic | shifting

Journal Article

Journal of Algebra, ISSN 0021-8693, 2008, Volume 320, Issue 1, pp. 426 - 436

Let be a finite abelian group that acts fixed point freely on a finite (solvable) group . Assume that is odd and is of squarefree exponent coprime to 6. We...

Solvable groups | Representations | Finite groups | Fixed point free action | MATHEMATICS | FINITE-GROUPS | representations | fixed point free action | finite groups | solvable groups

Solvable groups | Representations | Finite groups | Fixed point free action | MATHEMATICS | FINITE-GROUPS | representations | fixed point free action | finite groups | solvable groups

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 8/2015, Volume 42, Issue 1, pp. 1 - 23

Given a polynomial ring $$S = \Bbbk [x_1, \dots , x_n]$$ S = k [ x 1 , ⋯ , x n ] over a field $$\Bbbk $$ k , and a monomial ideal $$M$$ M of $$S$$ S , we say...

05E40 | 05D99 | Colored complexes | Mathematics | 13A02 | 13C05 | 13F55 | Clements–Lindström theorem | Macaulay-Lex rings | 13D40 | Convex and Discrete Geometry | Kruskal–Katona theorem | Hilbert function | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | 05E45 | f$$ f -vector | f-vector | MATHEMATICS | BETTI NUMBERS | COMPLEXES | Kruskal-Katona theorem | Clements-Lindstrom theorem | IDEALS

05E40 | 05D99 | Colored complexes | Mathematics | 13A02 | 13C05 | 13F55 | Clements–Lindström theorem | Macaulay-Lex rings | 13D40 | Convex and Discrete Geometry | Kruskal–Katona theorem | Hilbert function | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | 05E45 | f$$ f -vector | f-vector | MATHEMATICS | BETTI NUMBERS | COMPLEXES | Kruskal-Katona theorem | Clements-Lindstrom theorem | IDEALS

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 4/2008, Volume 27, Issue 2, pp. 215 - 245

We use the correspondence between hypergraphs and their associated edge ideals to study the minimal graded free resolution of squarefree monomial ideals. The...

Graded resolutions | Convex and Discrete Geometry | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Monomial ideals | Computer Science, general | Combinatorics | Hypergraphs | Regularity | Chordal graphs | MATHEMATICS | hypergraphs | graded resolutions | RESOLUTIONS | chordal graphs | regularity | monomial ideals

Graded resolutions | Convex and Discrete Geometry | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Monomial ideals | Computer Science, general | Combinatorics | Hypergraphs | Regularity | Chordal graphs | MATHEMATICS | hypergraphs | graded resolutions | RESOLUTIONS | chordal graphs | regularity | monomial ideals

Journal Article

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