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On conjugacy classes of Sn containing all irreducibles

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1 Published in 2018 at "Israel Journal of Mathematics"

DOI: 10.1007/s11856-018-1659-3

Abstract: It is shown that for the conjugation action of the symmetric group Sn, when n = 6 or n ≥ 8, all Sn-irreducibles appear as constituents of a single conjugacy class, namely, one indexed by… read more here.

Keywords: containing irreducibles; conjugacy classes; conjugacy; classes containing ... See more keywords

The structure of random homeomorphisms

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1 Published in 2017 at "Israel Journal of Mathematics"

DOI: 10.1007/s11856-020-2001-4

Abstract: In order to understand the structure of the “typical” element of a homeomorphism group, one has to study how large the conjugacy classes of the group are. When typical means generic in the sense of… read more here.

Keywords: conjugacy classes; haar; structure random; haar null ... See more keywords

Partial orders on conjugacy classes in the Weyl group and on unipotent conjugacy classes

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2 Published in 2021 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2021.107688

Abstract: Let $G$ be a reductive group over an algebraically closed field and let $W$ be its Weyl group. In a series of papers, Lusztig introduced a map from the set $[W]$ of conjugacy classes of… read more here.

Keywords: weyl group; orders conjugacy; partial orders; conjugacy classes ... See more keywords

Strictly transversal slices to conjugacy classes in algebraic groups

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1 Published in 2019 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2018.11.008

Abstract: Acknowledgements The author is grateful to Dave Benson for his help with the MAGMA software and to Institut des Hautes Etudes Scientifiques where this work was completed. read more here.

Keywords: classes algebraic; transversal slices; algebraic groups; strictly transversal ... See more keywords

The average element order and the number of conjugacy classes of finite groups

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1 Published in 2020 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2020.11.009

Abstract: Let $o(G)$ be the average order of the elements of $G$, where $G$ is a finite group. We show that there is no polynomial lower bound for $o(G)$ in terms of $o(N)$, where $N\trianglelefteq G$,… read more here.

Keywords: element order; order; average element; conjugacy classes ... See more keywords

Algebras with finitely many conjugacy classes of left ideals versus algebras of finite representation type

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0 Published in 2019 at "Journal of Pure and Applied Algebra"

DOI: 10.1016/j.jpaa.2019.01.010

Abstract: Let A be a finite dimensional algebra over an algebraically closed field with the radical nilpotent of index 2. It is shown that A has finitely many conjugacy classes of left ideals if and only… read more here.

Keywords: finite representation; finitely many; many conjugacy; classes left ... See more keywords

Two moonshines for L2(11) but none for M12

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0 Published in 2019 at "Nuclear Physics B"

DOI: 10.1016/j.nuclphysb.2019.01.004

Abstract: In this paper, we revisit an earlier conjecture by one of us that related conjugacy classes of $M_{12}$ to Jacobi forms of weight one and index zero. We construct Jacobi forms for all conjugacy classes… read more here.

Keywords: jacobi forms; two moonshines; conjugacy classes; moonshines none ... See more keywords

Algorithms for twisted conjugacy classes of polycyclic-by-finite groups

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0 Published in 2020 at "Topology and its Applications"

DOI: 10.1016/j.topol.2020.107565

Abstract: We construct two practical algorithms for twisted conjugacy classes of polycyclic-by-finite groups. The first algorithm determines whether two elements of a group are twisted conjugate for two given endomorphisms, under the condition that the Reidemeister… read more here.

Keywords: finite groups; classes polycyclic; twisted conjugacy; algorithms twisted ... See more keywords

On EPO-groups with a given property on their conjugacy classes

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1 Published in 2021 at "Communications in Algebra"

DOI: 10.1080/00927872.2021.1982956

Abstract: Abstract Let G be a finite group and V(G) be the set of all non-central conjugacy classes of G. Consider the conjugacy class graph of G which is defined as follows: its vertex set is… read more here.

Keywords: conjugacy; property conjugacy; conjugacy classes; given property ... See more keywords

Ideals and conjugacy classes in solvable lie algebras

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1 Published in 2022 at "International Journal of Geometric Methods in Modern Physics"

DOI: 10.1142/s021988782350202x

Abstract: A constructive procedure is given to determine all ideals of a solvable Lie algebra. This is used in determining algorithmically all conjugacy classes of subalgebras of a given solvable Lie algebra. read more here.

Keywords: classes solvable; conjugacy classes; lie algebras; solvable lie ... See more keywords

Maximal subgroups of the modular and other groups

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1 Published in 2018 at "Journal of Group Theory"

DOI: 10.1515/jgth-2018-0144

Abstract: Abstract In 1933 B. H. Neumann constructed uncountably many subgroups of SL2⁢(ℤ){{\rm SL}_{2}(\mathbb{Z})} which act regularly on the primitive elements of ℤ2{\mathbb{Z}^{2}}. As pointed out by Magnus, their images in the modular group PSL2⁢(ℤ)≅C3*C2{{\rm PSL}_{2}(\mathbb{Z})\cong C_{3}*C_{2}}… read more here.

Keywords: maximal subgroups; conjugacy classes; group; uncountably many ... See more keywords