Some Notes on Meet-Irreducible Subgroups of Finite Groups |
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| Authors: | Xiaolan Yi Alexander N Skiba |
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| Institution: | 1. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Chinayixiaolan2005@126.com;3. Department of Mathematics, Francisk Skorina Gomel State University, Gomel, Belarus |
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| Abstract: | A proper subgroup A of a finite group G is said to be primitive or meet-irreducible if there is a unique subgroup A0 ≤ G such that A is a maximal subgroup of A0. In this case we say that |A0: A| is the small index of A and denote it by |G: A|0. In this article, we study the influence of meet-irreducible subgroups and their small indexes on the structure of G. In particular, we prove that a finite group G is supersoluble if and only if |G: A|0 = |G: B|0 for any two meet-irreducible subgroups A and B of G with AG = BG. |
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| Keywords: | Finite group Meet-irreducible subgroup PST-group The small index |
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