Non-nilpotent subgroups of locally graded groups

Mohammad Zarrin

Non-nilpotent subgroups of locally graded groups

Group Theory 2014-12-05 v1

Authors: Mohammad Zarrin

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 $\le$ 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.

Keywords

nilpotent groups finite group theory combinatorial group theory

Cite

@article{arxiv.1412.1675,
  title  = {Non-nilpotent subgroups of locally graded groups},
  author = {Mohammad Zarrin},
  journal= {arXiv preprint arXiv:1412.1675},
  year   = {2014}
}

Comments

4 pages, to appear in Colloquium Mathematicum, 2015

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