ON GROUPS WITH A FINITE NUMBER OF NORMALIZERS

Authors

  • mohammad zarrin Department of Mathematics, University of Kurdistan, P.O. Box: 416, Sanandaj, Iran

Keywords:

Normalizer subgroups, Simple groups, n-Engel elements, Solu- ble groups

Abstract

The groups having exactly one normalizer are well-known. They are the Dedekind groups. All ï¬nite groups having exactly two normalizers were classiï¬ed by M.D. P´erez-Ramos and S. Camp-Mora generalized that re- sult to locally ï¬nite groups. Then M. Tota investigated the properties (such as solubility) of arbitrary groups with two, three and four normalizers. In this paper we prove that every ï¬nite group with at most 20 normalizers is soluble. Also we characterize all non-abelian simple (not necessarily ï¬nite) groups G with at most 57 normalizers. 10.1017/S000497271200007X

Published

2012-10-22

Issue

Vol. 86 No. 3 (2012)

Section

Articles
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