| Mar ’21 |
| 30 |
| 17:40 |
El próximo 30 de marzo de 2021 de 17.40 a 18.25, Ana Martínez Pastor pronunciará la charla «Hall-like theorems in products of π-decomposable groups» en el congreso Finite groups in Valencia. Más información en
Archivo de la etiqueta: product of groups
Paper «On products of groups and indices not divisible by a given prime» published in Monatsh. Math.
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María José Felipe, Lev S. Kazarin, Ana Martínez-Pastor, and Víctor Sotomayor.
On products of groups and indices not divisible by a given prime.
Comm. Algebra, 193(4):811–827, 2020.
doi:10.1007/s00605-020-01446-z
Abstract
Let the group G = AB be the product of subgroups A and B, and let p be a prime. We prove that p does not divide the conjugacy class size (index) of each p-regular element of prime power order x ∈ A ∪ B if and only if G is p-decomposable, i.e. G=Op(G) × Op’(G).
2020 Mathematics Subject Classification: 20D40, 20E45, 20D20, 20D60
Keywords: Finite groups; products of groups; conjugacy classes; p-structure; prime graph; almost simple groups
Talk «Thompson-like characterization of solubility for products of groups» at 2020 Zassenhaus Groups and Friends Conference
| May ’20 |
| 29 |
| 15:55 |
María Dolores Pérez Ramos will give the talk entitled
Thompson-like characterization of solubility for products of groups
at the 2020 Zassenhaus Groups and Friends Conference online on 29th May 2020 at 15.55. The link for the talk and its recording appear on http://www2.math.binghamton.edu/p/zassenhaus/zassenhaus_2020/home.
Abstract
A remarkable result of Thompson states that a finite group is soluble if
and only if its two-generated subgroups are soluble. This result has been
sharply generalized, and it is in the core of a wide area of study in the theory
of groups, aiming for global properties of groups from local properties of two-
generated (or more generally, n-generated) subgroups. We report about an
extension of Thompson’s theorem from the perspective of factorized groups.
We prove that for a finite group G = AB, with A, B subgroups of G, if ha, bi
is soluble for all a ∈ A and all b ∈ B, then [A, B] is soluble. In that case, the
group G is said to be an S-connected product of the subgroups A and B, for
the class S of all finite soluble groups. As an application, deep results about
connected products of finite soluble groups, for other relevant classes of
groups, are extended to the finite universe. Collaboration with M. P. Gállego (U.
Zaragoza, Spain), P. Hauck (U. Tübingen, Germany), L. Kazarin (U. Yaroslavl,
Russia), A. Martı́nez-Pastor (U. Politècnica de València, Spain) .