Product of finitely-connected abelian groups

Sesekin, N. F.

doi:10.1007/bf02196460

Cited by 14 publications

(8 citation statements)

References 3 publications

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“…The next result can essentially be found in both Sesekin [3] and Schenkman [4]. Finally this last lemma, which can be found in Schenkman [4], will turn out to be crucial.…”

mentioning

confidence: 66%

Normal subgroups of groups which are products of two Abelian subgroups

Knop¹

1973

Proc. Amer. Math. Soc.

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Abstract.It is shown that if a group G=AB, where A and B are Abelian subgroups of G, A^B, and either A or B satisfies the maximum condition, then there is a normal subgroup N of G, N^G, such that N contains either A or B.Summary and background.The purpose of this paper is to show that, if a group G is a nontrivial product of two Abelian subgroups A and B, and if either A or B satisfies the maximum condition, then there is a proper normal subgroup of G containing either A or B. (L. E. Knop [7]).The basic impetus for this research is found in a paper of N. Itô [1]. In this paper, Itô showed that if G is a product of two Abelian subgroups A and B, then G is metabelian. Furthermore, he showed that if G is finite, then there is a normal subgroup of G, not the identity, which is contained in either A or B, and also that there is a proper normal subgroup of G which contains either A or B.Additional work on the problem of when there is a normal subgroup contained in one of the two factors has been done by P. M. Cohn

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“…The next result can essentially be found in both Sesekin [3] and Schenkman [4]. Finally this last lemma, which can be found in Schenkman [4], will turn out to be crucial.…”

mentioning

confidence: 66%

Normal subgroups of groups which are products of two Abelian subgroups

Knop¹

1973

Proc. Amer. Math. Soc.

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“…If GIG' has finite sectional rank, it follows as in the proof of (13) that A and B have finite sectional rank. This contradicts (11). (15) If GIG' has finite torsionfree rank, it follows as in the proof of (13) that A and B have finite torsionfree rank.…”

Section: Bernhard Ambergmentioning

confidence: 87%

On groups which are the product of abelian subgroups

Amberg

1985

Glasgow Math. J.

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“…But it seems to be unknown at present, whether G satisfies the minimum condition on all its subgroups or likewise must even be a Chernikov group. If A and B are abelian with minimum condition on subgroup, then this is the case, as N. Sesekin has shown in [32]. Also in the case that the two Chernikov subgroups A and B both containing abelian subgroups of index at most 2, more can be said.…”

Section: Theorem 73 (Amberg and Sysak 2008mentioning

confidence: 91%