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Group Theory

New submissions

[ total of 15 entries: 1-15 ]
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New submissions for Tue, 20 Mar 18

[1]  arXiv:1803.06679 [pdf, ps, other]
Title: Kirchberg--Wassermann exactness vs exactness: reduction to the unimodular totally disconnected case
Comments: 7 pages
Subjects: Group Theory (math.GR); Operator Algebras (math.OA)

We show that in order to prove that every second countable locally compact groups with exact reduced group C*-algebra is exact in the dynamical sense (i.e. KW-exact) it suffices to show this for totally disconnected groups.

[2]  arXiv:1803.06691 [pdf, ps, other]
Title: On the Absence of a Normal Nonabelian Sylow Subgroup
Comments: 6 pages, 1 figure
Subjects: Group Theory (math.GR)

Let $G$ be a finite solvable group. We show that $G$ does not have a normal nonabelian Sylow $p$-subgroup when its prime character degree graph $\Delta(G)$ satisfies a technical hypothesis.

[3]  arXiv:1803.06872 [pdf, ps, other]
Title: The group generated by Riordan involutions
Comments: 18 pages
Subjects: Group Theory (math.GR)

We prove that any element in the group generated by the Riordan involutions is the product of at most four of them. We also give a description of this subgroup as a semidirect product of a special subgroup of the commutator subgroup and the Klein four-group.

Cross-lists for Tue, 20 Mar 18

[4]  arXiv:1803.06463 (cross-list from math.QA) [pdf, ps, other]
Title: Multiplication formulas and semisimplicity for q-Schur superalgebras
Comments: 22 pages. Nagoya J. Math. (to appear)
Subjects: Quantum Algebra (math.QA); Group Theory (math.GR); Rings and Algebras (math.RA); Representation Theory (math.RT)

We investigate products of certain double cosets for the symmetric group and use the findings to derive some multiplication formulas for q-Schur superalgebras. This gives a combinatorialisation of the relative norm approach developed by the first two authors. We then give several applications of the multiplication formulas, including the matrix representation of the regular representation and a semisimplicity criterion for q-Schur superalgebras. We also construct infinitesimal and little q-Schur superalgebras directly from the multiplication formulas and develop their semisimplicity criteria.

[5]  arXiv:1803.06712 (cross-list from math.GN) [pdf, ps, other]
Title: Haar-$\mathcal I$ sets: looking at small sets in Polish groups through compact glasses
Comments: 44 pages
Subjects: General Topology (math.GN); Group Theory (math.GR)

Generalizing Christensen's notion of a Haar-null set and Darji's notion of a Haar-meager set, we introduce and study the notion of a Haar-$\mathcal I$ set in a Polish group. Here $\mathcal I$ is an ideal of subsets of some compact metrizable space $K$. A Borel subset $B\subset X$ of a Polish group $X$ is called Haar-$\mathcal I$ if there exists a continuous map $f:K\to X$ such that $f^{-1}(B+x)\in\mathcal I$ for all $x\in X$. Moreover, $B$ is generically Haar-$\mathcal I$ if the set of witness functions $\{f\in C(K,X):\forall x\in X\;\;f^{-1}(B+x)\in\mathcal I\}$ is comeager in the function space $C(K,X)$. We study (generically) Haar-$\mathcal I$ sets in Polish groups for many concrete and abstract ideals $\mathcal I$, and construct the corresponding distinguishing examples. Also we establish various Steinhaus properties of the families of (generically) Haar-$\mathcal I$ sets in Polish groups for various ideals $\mathcal I$.

[6]  arXiv:1803.06715 (cross-list from math.AC) [pdf, ps, other]
Title: Restricting homology to hypersurfaces
Comments: 17 pages. To appear in "Geometric and topological aspects of the representation theory of finite groups", to be published by Springer in the series titled "Proceedings in Mathematics"
Subjects: Commutative Algebra (math.AC); Group Theory (math.GR)

This paper concerns the homological properties of a module $M$ over a commutative noetherian ring $R$ relative to a presentation $R\cong P/I$, where $P$ is local ring. It is proved that the Betti sequence of $M$ with respect to $P/(f)$ for a regular element $f$ in $I$ depends only on the class of $f$ in $I/\mathfrak{n} I$, where $\mathfrak{n}$ is the maximal ideal of $P$. Applications to the theory of supports sets in local algebra and in the modular representation theory of elementary abelian groups are presented.

[7]  arXiv:1803.06965 (cross-list from math.AG) [pdf, ps, other]
Title: The normal hull and commutator group for nonconnected group schemes
Authors: Giulia Battiston
Comments: 4 pages, comments are welcome
Subjects: Algebraic Geometry (math.AG); Group Theory (math.GR)

In this short note, we prove that there is a well behaved notion of normal hull for smooth algebraic group schemes over a field and that the commutator group $(G,H)$ is well defined for $H\subset G$ smooth, even when both of them are not connected.

Replacements for Tue, 20 Mar 18

[8]  arXiv:1507.04915 (replaced) [pdf, other]
Title: The boundary model for the continuous cohomology of Isom$^+(\mathbb{H}^n)$
Authors: Hester Pieters
Comments: 25 pages, 1 figure, changed title, revised and extended version
Subjects: Group Theory (math.GR); Algebraic Topology (math.AT)
[9]  arXiv:1604.01938 (replaced) [pdf, ps, other]
Title: On the Noether number of $p$-groups
Comments: Several corrections and simplifications made
Subjects: Group Theory (math.GR); Commutative Algebra (math.AC); Number Theory (math.NT); Representation Theory (math.RT)
[10]  arXiv:1605.07879 (replaced) [pdf, ps, other]
Title: Cubulating mapping tori of polynomial growth free group automorphisms
Comments: The proof has been significantly simplified
Subjects: Group Theory (math.GR)
[11]  arXiv:1707.05530 (replaced) [pdf, ps, other]
Title: Chain varieties of monoids
Comments: 76 pages, 3 figures, 3 tables. In comparison with the previous version, we made a number of linguistic corrections only
Subjects: Group Theory (math.GR)
[12]  arXiv:1709.09278 (replaced) [pdf, other]
Title: Classifying Character Degree Graphs With 6 Vertices
Comments: 18 pages. arXiv admin note: text overlap with arXiv:1707.03020
Subjects: Group Theory (math.GR); Representation Theory (math.RT)
[13]  arXiv:1801.01165 (replaced) [pdf, other]
Title: Automorphism groups and Ramsey properties of sparse graphs
Comments: 40 pages, 3 figures, new proof of Theorem 3.19 and other minor revisions
Subjects: Group Theory (math.GR); Discrete Mathematics (cs.DM); Combinatorics (math.CO); Dynamical Systems (math.DS); Logic (math.LO)
[14]  arXiv:1801.02932 (replaced) [pdf, ps, other]
Title: Polynomials describing the multiplication in finitely generated torsion free nilpotent groups
Subjects: Group Theory (math.GR)
[15]  arXiv:1802.07049 (replaced) [pdf, ps, other]
Title: The Bieri-Neumann-Strebel invariants via Newton polytopes
Authors: Dawid Kielak
Comments: 39 pages, no figures. v2. improved exposition
Subjects: Group Theory (math.GR); Geometric Topology (math.GT); Rings and Algebras (math.RA)
[ total of 15 entries: 1-15 ]
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