2016, Mathematical surveys and monographs, ISBN 9781470429010, Volume no. 215., xvii, 174 pages

"Richard Thompson's famous group FF has the striking property that it can be realized as a dense subgroup of the group of all orientation-preserving homeomorphisms of the unit interval, but it can...

Geometric group theory | Dimension theory (Algebra) | Homeomorphisms | Numbers, Real

Geometric group theory | Dimension theory (Algebra) | Homeomorphisms | Numbers, Real

Book

2017, Mathematical surveys and monographs, ISBN 9781470434823, Volume 217, 2 volumes

Book

2015, London Mathematical Society lecture note series, ISBN 1107442885, Volume 416, xii, 281

Reversibility is a thread woven through many branches of mathematics. It arises in dynamics, in systems that admit a time-reversal symmetry, and in group theory...

Conjugacy classes | Reverse mathematics | Dynamics | Automorphisms | Group theory

Conjugacy classes | Reverse mathematics | Dynamics | Automorphisms | Group theory

Book

Monatshefte für Mathematik, ISSN 0026-9255, 5/2019, Volume 189, Issue 1, pp. 1 - 21

... ) of a group G we determine several subgroups of $$\mathrm{Aut}(Q)$$ Aut ( Q ) and find necessary and sufficient conditions for these subgroups to coincide with the whole group $$\mathrm{Aut}(Q)$$ Aut ( Q...

20B25 | Automorphism of a quandle | Braid group | 20N02 | 57M27 | Quandle | Mathematics, general | Mathematics | Coxeter group | Enveloping group | MATHEMATICS

20B25 | Automorphism of a quandle | Braid group | 20N02 | 57M27 | Quandle | Mathematics, general | Mathematics | Coxeter group | Enveloping group | MATHEMATICS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2019, Volume 371, Issue 1, pp. 105 - 136

...: automorphisms and the size of minimal generating sets. In order to do this, we examine the k-homogeneous permutation groups...

primitive groups | AUTOMORPHISM-GROUPS | GENERATORS | regular semigroups | PERMUTATION-GROUPS | ENDOMORPHISM SEMIGROUPS | CLASSIFICATION | NILPOTENT RANKS | MONOIDS | automorphisms of semigroups | CATEGORIES | Transformation semigroups | rank of semigroups | MATHEMATICS | homogeneous groups | permutation groups | TRANSITIVE COLLINEATION GROUPS | TRANSFORMATIONS

primitive groups | AUTOMORPHISM-GROUPS | GENERATORS | regular semigroups | PERMUTATION-GROUPS | ENDOMORPHISM SEMIGROUPS | CLASSIFICATION | NILPOTENT RANKS | MONOIDS | automorphisms of semigroups | CATEGORIES | Transformation semigroups | rank of semigroups | MATHEMATICS | homogeneous groups | permutation groups | TRANSITIVE COLLINEATION GROUPS | TRANSFORMATIONS

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 12/2017, Volume 28, Issue 14, p. 1750101

.... We give a semidirect product topological characterization on the isometry group of a twisted reduced group C...

Spectral triple | Twisted reduced group C∗ -algebra | Filtration | Discrete group | Isometry group | MATHEMATICS | filtration | twisted reduced group C-algebra | isometry group | spectral triple | QUANTUM METRIC-SPACES | FREDHOLM MODULES | Algebra

Spectral triple | Twisted reduced group C∗ -algebra | Filtration | Discrete group | Isometry group | MATHEMATICS | filtration | twisted reduced group C-algebra | isometry group | spectral triple | QUANTUM METRIC-SPACES | FREDHOLM MODULES | Algebra

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 12/2017, Volume 184, Issue 4, pp. 519 - 530

Let G be a group and $$\varphi \in {\text {Aut}}(G)$$ φ ∈ Aut ( G ) . Then the set G equipped with the binary operation $$a*b=\varphi (ab^{-1})b$$ a ∗ b = φ ( a b - 1...

Central automorphism | Automorphism of quandle | Two-point homogeneous quandle | Knot quandle | 57M27 | Secondary 20B25 | Mathematics, general | Mathematics | Primary 20N02 | Connected quandle | ALEXANDER QUANDLES | MATHEMATICS

Central automorphism | Automorphism of quandle | Two-point homogeneous quandle | Knot quandle | 57M27 | Secondary 20B25 | Mathematics, general | Mathematics | Primary 20N02 | Connected quandle | ALEXANDER QUANDLES | MATHEMATICS

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 2016, Volume 298, pp. 612 - 653

We introduce the algebraic entropy for endomorphisms of arbitrary abelian groups, appropriately modifying existing notions of entropy...

Lehmer problem | Abelian group | Group endomorphism | Discrete dynamical system | Mahler measure | Algebraic entropy | Addition Theorem | MATHEMATICS | LCA GROUPS | SPACES | AUTOMORPHISMS | ENDOMORPHISMS

Lehmer problem | Abelian group | Group endomorphism | Discrete dynamical system | Mahler measure | Algebraic entropy | Addition Theorem | MATHEMATICS | LCA GROUPS | SPACES | AUTOMORPHISMS | ENDOMORPHISMS

Journal Article

Inventiones mathematicae, ISSN 1432-1297, 2014, Volume 199, Issue 3, pp. 805 - 858

We give algebraic characterizations for expansiveness of algebraic actions of countable groups. The notion of $$p...

37B40 | 43A20 | Secondary 22D15 | Mathematics, general | 37A15 | Mathematics | Primary 22D40 | 20C07 | MATHEMATICS | FUGLEDE-KADISON DETERMINANTS | ZERO DIVISORS | INDEPENDENCE | DYNAMICS | AMENABLE-GROUPS | GROUP AUTOMORPHISMS | Z(D)-ACTIONS | LOCAL ENTROPY THEORY | COMPACT ABELIAN-GROUPS | PAIRS | Algebra | Mathematical analysis | Group theory | Texts | Entropy | Automorphisms | Expansion | Subgroups

37B40 | 43A20 | Secondary 22D15 | Mathematics, general | 37A15 | Mathematics | Primary 22D40 | 20C07 | MATHEMATICS | FUGLEDE-KADISON DETERMINANTS | ZERO DIVISORS | INDEPENDENCE | DYNAMICS | AMENABLE-GROUPS | GROUP AUTOMORPHISMS | Z(D)-ACTIONS | LOCAL ENTROPY THEORY | COMPACT ABELIAN-GROUPS | PAIRS | Algebra | Mathematical analysis | Group theory | Texts | Entropy | Automorphisms | Expansion | Subgroups

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2015, Volume 17, Issue 11, pp. 2903 - 2947

We give a complete characterization of the locally compact groups that are nonelementary Gromov-hyperbolic and amenable...

Gromov hyperbolic group | Locally compact group | Amenable group | Compacting automorphisms | Contracting automorphisms | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | contracting automorphisms | amenable group | AUTOMORPHISMS | BOUNDARY | CONTRACTION GROUPS | locally compact group | compacting automorphisms | Mathematics - Group Theory

Gromov hyperbolic group | Locally compact group | Amenable group | Compacting automorphisms | Contracting automorphisms | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | contracting automorphisms | amenable group | AUTOMORPHISMS | BOUNDARY | CONTRACTION GROUPS | locally compact group | compacting automorphisms | Mathematics - Group Theory

Journal Article

Semigroup forum, ISSN 1432-2137, 2017, Volume 96, Issue 1, pp. 178 - 196

We study the structure of groups of finitary tropical matrices under multiplication...

Algebra | Tropical matrices | Semigroups | Tropical polytopes | Mathematics | Automorphism group | Green’s relations | MATHEMATICS | Green's relations | RANK

Algebra | Tropical matrices | Semigroups | Tropical polytopes | Mathematics | Automorphism group | Green’s relations | MATHEMATICS | Green's relations | RANK

Journal Article

12.
Full Text
Finite p-groups with a Frobenius group of automorphisms whose kernel is a cyclic p-group

Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2015, Volume 143, Issue 5, pp. 1837 - 1848

Suppose that a finite p admits a Frobenius group of automorphisms FH that is a cyclic p...

Automorphism | Lie ring | Frobenius group | Finite p-group | Nilpotency class | LIE-ALGEBRAS | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | nilpotency class | RINGS | automorphism

Automorphism | Lie ring | Frobenius group | Finite p-group | Nilpotency class | LIE-ALGEBRAS | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | nilpotency class | RINGS | automorphism

Journal Article

2014, Volume 629.

Conference Proceeding

Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2016, Volume 144, Issue 10, pp. 4135 - 4150

The main result of this paper is a complete classification of the outer automorphism groups of two-generator, one-relator groups with torsion...

Nielsen equivalence | One-relator groups | Outer automorphism groups | MATHEMATICS | MATHEMATICS, APPLIED | HYPERBOLIC GROUPS | outer automorphism groups | 1-RELATOR GROUPS | FREE PRODUCT | SUBGROUPS | Mathematics - Group Theory

Nielsen equivalence | One-relator groups | Outer automorphism groups | MATHEMATICS | MATHEMATICS, APPLIED | HYPERBOLIC GROUPS | outer automorphism groups | 1-RELATOR GROUPS | FREE PRODUCT | SUBGROUPS | Mathematics - Group Theory

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 11/2019, Volume 50, Issue 3, pp. 293 - 315

We study the homology of an explicit finite-index subgroup of the automorphism group of a partially commutative group, in the case when its defining graph is a tree...

Trees | Mathematics | Betti numbers | Automorphism groups | 20F65 | Lower bounds | Symbolic method | Exponential generating functions | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | RAAGs

Trees | Mathematics | Betti numbers | Automorphism groups | 20F65 | Lower bounds | Symbolic method | Exponential generating functions | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | RAAGs

Journal Article

Selecta mathematica (Basel, Switzerland), ISSN 1420-9020, 2017, Volume 24, Issue 2, pp. 1453 - 1478

We compute the groups $$H^*(\mathrm {Aut}(F_n); M)$$ H∗(Aut(Fn);M) and $$H^*(\mathrm {Out}(F_n); M)$$ H∗(Out(Fn);M) in a stable range, where M is obtained by applying a Schur functor...

Homology stability | Automorphisms of free groups | 20J06 | Mathematics, general | 20F28 | Mathematics | 57R20 | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | HOMOLOGY | SURFACES | GRAPHS

Homology stability | Automorphisms of free groups | 20J06 | Mathematics, general | 20F28 | Mathematics | 57R20 | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | HOMOLOGY | SURFACES | GRAPHS

Journal Article

The bulletin of symbolic logic, ISSN 1943-5894, 2014, Volume 14, Issue 4, pp. 449 - 480

This is an introductory survey of the emerging theory of two new classes of (discrete, countable) groups, called hyperlinear and sofic groups...

Ultraproducts | Von Neumann algebra | Algebra | Natural numbers | Ultrapowers | Topology | Banach space | Algebraic topology | Topological spaces | MATHEMATICS | EXACTNESS | ULTRAPRODUCTS | CELLULAR-AUTOMATA | CENTRAL-SEQUENCES | REPRESENTATIONS | TENSOR-PRODUCTS | C-ASTERISK-ALGEBRAS | AMENABILITY | AUTOMORPHISMS | LOGIC | CONJECTURE | 03C20 | 20F69 | 37B10 | 46L10

Ultraproducts | Von Neumann algebra | Algebra | Natural numbers | Ultrapowers | Topology | Banach space | Algebraic topology | Topological spaces | MATHEMATICS | EXACTNESS | ULTRAPRODUCTS | CELLULAR-AUTOMATA | CENTRAL-SEQUENCES | REPRESENTATIONS | TENSOR-PRODUCTS | C-ASTERISK-ALGEBRAS | AMENABILITY | AUTOMORPHISMS | LOGIC | CONJECTURE | 03C20 | 20F69 | 37B10 | 46L10

Journal Article

Combinatorica (Budapest. 1981), ISSN 1439-6912, 2015, Volume 36, Issue 4, pp. 371 - 393

Let A be an abelian group and let ι be the automorphism of A defined by: ι: a ↦ a−1. A Cayley graph Γ = Cay(A,S) is said to have an automorphism group as small as possible if Aut...

20B25 | Mathematics, general | Mathematics | 05E18 | Combinatorics | MATHEMATICS | PERMUTATION-GROUPS | SCHUR RINGS | CYCLIC GROUPS | REGULAR REPRESENTATIONS

20B25 | Mathematics, general | Mathematics | 05E18 | Combinatorics | MATHEMATICS | PERMUTATION-GROUPS | SCHUR RINGS | CYCLIC GROUPS | REGULAR REPRESENTATIONS

Journal Article

ALGEBRAIC AND GEOMETRIC TOPOLOGY, ISSN 1472-2739, 2019, Volume 19, Issue 4, pp. 1747 - 1835

For every group G, we define the set of hyperbolic structures on G, denoted by H...

GRAPH | MATHEMATICS | TREES | BOUNDED COHOMOLOGY | ACCESSIBILITY | SQ-UNIVERSALITY | AUTOMORPHISMS | SUBGROUPS | COMBINATION | GEOMETRY

GRAPH | MATHEMATICS | TREES | BOUNDED COHOMOLOGY | ACCESSIBILITY | SQ-UNIVERSALITY | AUTOMORPHISMS | SUBGROUPS | COMBINATION | GEOMETRY

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 6/2019, Volume 87, Issue 6, pp. 1227 - 1235

In this paper we propose an isomorphism criterion for cyclic balanced configurations defined over the same group $$\mathbb {Z}_n$$ Z n...

20B25 | Information and Communication, Circuits | Cyclic group | 20B10 | Discrete Mathematics in Computer Science | Computer Science | Coding and Information Theory | Cryptology | CI-property | Balanced configuration | Cayley object | Data Structures and Information Theory | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

20B25 | Information and Communication, Circuits | Cyclic group | 20B10 | Discrete Mathematics in Computer Science | Computer Science | Coding and Information Theory | Cryptology | CI-property | Balanced configuration | Cayley object | Data Structures and Information Theory | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

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