Archivo por meses: julio 2020

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

Paper «The abelian kernel of an inverse semigroup» published in Mathematics

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Adolfo Ballester-Bolinches, Vicent Pérez-Calabuig.
The abelian kernel of an inverse semigroup.
Mathematics, 8(8):1219 (12 pages), 2020.

doi:10.3390/math8081219

Abstract

The problem of computing the abelian kernel of a finite semigroup was first solved by Delgado describing an algorithm that decides whether a given element of a finite semigroup S belongs to the abelian kernel. Steinberg extended the result for any variety of abelian groups with decidable membership. In this paper, we used a completely different approach to complete these results by giving an exact description of the abelian kernel of an inverse semigroup. An abelian group that gives this abelian kernel was also constructed.

2020 Mathematics Subject Classification: 20M10, 20M17

Keywords: finite semigroup; abelian kernels; profinite topologies; partial automorphisms; extension problem