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A note on infinite aS-groups

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Abstract

Let G be a group. If every nontrivial subgroup of G has a proper supplement, then G is called an aS-group. We study some properties of aS-groups. For instance, it is shown that a nilpotent group G is an aS-group if and only if G is a subdirect product of cyclic groups of prime orders. We prove that if G is an aS-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 aS-group. Finally, it is shown that if G is an aS-group and |G| ≠ pq, p, where p and q are primes, then G has a triple factorization.

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Authors and Affiliations

  1. Department of Basic Sciences, Jundi-Shapur University of Technology, P.O. Box 64615-334, Dezful, Iran

    Reza Nikandish

  2. Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany

    Babak Miraftab

Authors
  1. Reza Nikandish
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  2. Babak Miraftab
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Correspondence to Reza Nikandish.

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Nikandish, R., Miraftab, B. A note on infinite aS-groups. Czech Math J 65, 1003–1009 (2015). https://doi.org/10.1007/s10587-015-0223-0

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  • DOI: https://doi.org/10.1007/s10587-015-0223-0

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