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

Paper “Groups with every subgroup ascendant-by-finite” published in Cent. Eur. J. Math.

The following paper has been published.

El siguiente artículo ha sido publicado.

El següent article ha sigut publicat.

Sergio Camp-Mora

Groups with every subgroup ascendant-by-finite

Cent. Eur. J. Math., 11(12), 2182-2185 (2013)

http://dx.doi.org/10.2478/s11533-013-0312-y

Abstract: A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.

MSC:  20F19, 20F22, 20F50
Keywords: Ascendant subgroup, Locally nilpotent, Radical, Locally finite group