Artinian Modules over Group Rings

Otal, Javier; Subbotin, Igor Ya.; Kurdachenko, Leonid A.

doi:10.1007/978-3-7643-7765-6

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Cited by 3 publications

References 151 publications

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On a generalization of Baer Theorem

Kurdachenko

Otal

Subbotin

2013

Proc. Amer. Math. Soc.

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R. Baer has proved that if the factor-group G/ζ n (G) of a group G by the member ζ n (G) of its upper central series is finite (here n is a positive integer) then the member γ n+1 (G) of the lower central series of G is also finite. In particular, in this case, the nilpotent residual of G is finite. This theorem admits the following simple generalization that has been published very recently by M. de Falco, F. de Giovanni, C. Musella and Ya. P. Sysak: "If the factor-group G/Z of a group G modulo its upper hypercenter Z is finite then G has a finite normal subgroup L such that G/L is hypercentral". In the current article we offer a new simpler very short proof of this theorem and specify it substantially. In fact, we prove that if |G/Z| = t then |L| ≤ t k , where k = 1 2 (logpt + 1), and p is the least prime divisor of t.

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