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Nonnormal and minimal nonabelian subgroups of a finite group

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Abstract

The main aim of this paper is to show how minimal nonabelian subgroups may be used to prove some deep results of finite group theory. The second aim is to offer new proofs of some characterization theorems. Among them are theorems of Z. Janko, O. Schmidt and D. Passman. A number of new results is proved; for example, we obtained the classification of non-nilpotent groups without three nonnormal subgroups of pairwise distinct orders.

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Authors and Affiliations

  1. Department of Mathematics, University of Haifa Mount Carmel, Haifa, 31905, Israel

    Yakov Berkovich

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  1. Yakov Berkovich
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Correspondence to Yakov Berkovich.

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Dedicated to I. Martin Isaacs on the occasion of his seventieth birthday

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Berkovich, Y. Nonnormal and minimal nonabelian subgroups of a finite group. Isr. J. Math. 180, 371–412 (2010). https://doi.org/10.1007/s11856-010-0108-8

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  • DOI: https://doi.org/10.1007/s11856-010-0108-8

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