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A note on infinite a S -groups

Reza Nikandish, Babak Miraftab (2015)

Czechoslovak Mathematical Journal

Let G be a group. If every nontrivial subgroup of G has a proper supplement, then G is called an a S -group. We study some properties of a S -groups. For instance, it is shown that a nilpotent group G is an a S -group if and only if G is a subdirect product of cyclic groups of prime orders. We prove that if G is an a S -group which satisfies the descending chain condition on subgroups, then G is finite. Among other results, we characterize all abelian groups for which every nontrivial quotient group is an a S -group....

Calculating the genus of a direct product of certain nilpotent groups.

Peter Hilton, Dirk Scevenels (1995)

Publicacions Matemàtiques

The Mislin genus G(N) of a finitely generated nilpotent group N with finite commutator subgroup admits an abelian group structure. If N satisfies some additional conditions -we say that N belongs to N1- we know exactly the structure of G(N). Considering a direct product N1 x ... x Nk of groups in N1 takes us virtually always out of N1. We here calculate the Mislin genus of such a direct product.

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