Non-nilpotent subgroups of locally graded groups

2014/12/04 by Mohammad Zarrin, Zarrin, Mohammad
Mathematics · #20E99 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20E99

paper · pdf · doi:10.48550/arxiv.1412.1675

4 pages, to appear in Colloquium Mathematicum, 2015

arxiv created 2014/12/04 · arxiv updated 2014/12/05

Abstract

In this paper, we show that a locally graded group with a finite number m of non-(nilpotent of class at most n) subgroups is (soluble of class at most [log2(n)] + m + 3)-by-(finite of order ≤ m!). Also we show that the derived length of a soluble group with a finite number m of non-(nilpotent of class at most n) subgroups, is at most [log2(n)] + m + 1.

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