Paper “On p-nilpotency of hyperfinite groups” published in Monatsh. Math.

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A. Ballester-Bolinches, S. Camp-Mora, and F. Spagnuolo

On p-nilpotency of hyperfinite groups

Monatsh. Math., 176(4) (2015), 497–502

http://dx.doi.org/10.1007/s00605-014-0633-3

Abstract

Let p be a prime. We say that class X of hyperfinite p-groups determines p-nilpotency locally if every finite group G with a Sylow p-subgroup P in X is p-nilpotent if and only if N_G(P) is p-nilpotent. The results of this paper improve a recent result of Kurdachenko and Otal and show that if a hyperfinite group G has a pronormal Sylow p-subgroup in X, then G is p-nilpotent if and only if N_G(P) is p-nilpotent provided that X is closed under taking subgroups and epimorphic images. If X is not closed under taking epimorphic images, we have to impose local p-solubility to G. In this case, the hypothesis of pronormality can be removed.

2010 Mathematics subject classification: 20E15, 20F19, 20F22

Keywords: locally finite group; hyperfinite group; p-nilpotency

Paper “A note on Sylow permutable subgroups of infinite groups” published in J. Algebra

The following paper has been published.

El siguiente artículo ha sido publicado.

El següent article ha sigut publicat.

A. Ballester-Bolinches, S. Camp-Mora, L. A. Kurdachenko

A note on Sylow permutable subgroups of infinite groups

J. Algebra, 398, 156-161 (2014)

http://dx.doi.org/10.1016/j.jalgebra.2013.08.042

Abstract: A subgroup A of a periodic group G is said to be Sylow permutable,
or S-permutable, subgroup of G if A P = P A for all Sylow subgroups
P of G. The aim of this paper is to establish the local nilpotency
of the section A^G /Core_G( A) for an S-permutable subgroup A of a
locally finite group G.
MSC: 20E15, 20F19, 20F22
Keywords: Locally finite group, Hyperfinite group, Sylow permutability, Ascendant subgroup