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Bounds for the Number of Conjugacy Classes of Non-Normal Subgroups in a Finite p -Group

✍ Scribed by Fernández-Alcober, Gustavo A.; Legarreta, Leire

Book ID
127327202
Publisher
Taylor and Francis Group
Year
2009
Tongue
English
Weight
181 KB
Volume
37
Category
Article
ISSN
0092-7872

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Let ν G denote the number of conjugacy classes of non-normal subgroups of a group G We prove that if G is a finite group and ν G = 0 then there is a cyclic subgroup C of prime power order contained in the centre of G such that the order of G/C is a product of at most ν G + 1 primes. We also obtain a

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For a finite group G, let k G denote the number of conjugacy classes of G. We prove that a simple group of Lie type of untwisted rank l over the field of q Ž . l elements has at most 6 q conjugacy classes. Using this estimate we show that for Ž . Ž . 10 n completely reducible subgroups G of GL n, q