Displaying similar documents to “Infinite locally finite groups of type PSL(2,K) or Sz(K) are not minimal under certain conditions.”

Locally graded groups with certain minimal conditions for subgroups (II).

Javier Otal, Juan Manuel Peña (1988)

Publicacions Matemàtiques

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This paper deals with one of the ways of studying infinite groups many of whose subgroups have a prescribed property, namely the consideration of minimal conditions. If P is a theoretical property of groups and subgroups, we show that a locally graded group P satisfies the minimal conditions for subgroups not having P if and only if either G is a Cernikov group or every subgroup of G satisfies P, for certain values of P concerning normality, nilpotency and related ideas.

On totally inert simple groups

Martyn Dixon, Martin Evans, Antonio Tortora (2010)

Open Mathematics

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A subgroup H of a group G is inert if |H: H ∩ H g| is finite for all g ∈ G and a group G is totally inert if every subgroup H of G is inert. We investigate the structure of minimal normal subgroups of totally inert groups and show that infinite locally graded simple groups cannot be totally inert.

On the derived length of parasoluble groups

Alessio Russo (2003)

Bollettino dell'Unione Matematica Italiana

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In this paper groups are considered inducing groups of power automorphisms on each factor of their derived series. In particular, it is proved that soluble groups with such property have derived length at most 3, and that this bound is best possible.