Bulletin of the Malaysian Mathematical Sciences Society, ( ISI ), Volume (47), No (2), Year (2024-1)

Title : ( Bounds for the Generalization of Baer’s Type Theorems )

Authors: Yasaman Taghavi , Saeed Kayvanfar ,

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Abstract

A well-known theorem of Baer states that in a given group G, the (n + 1)th term of the lower central series of G is finite when the index of the nth term of the upper central series is finite. Recently, Kurdachenko and Otal proved a similar statement for this theorem when the upper hypercenter factor of a locally generalized radical group has finite special rank. In this paper, we first decrease the Ellis’ bound obtained for the order of γn+1(G). Then we extend Kurdachenko’s result for locally generalized radical groups. Moreover, some new upper bounds for the special rank of γn+1(G, A) are also given, where A is a subgroup of automorphisms of G which contains inner automorphisms of G.

Keywords

Baer’s theorem; Hypercenter; Special rank; Locally generalized radical group.