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On the Fitting length of generalized Hughes subgroup. (English) Zbl 0674.20007

In the search of reasonable generalizations of a result of A. Espuelas [J. Algebra 105, 365-371 (1987; Zbl 0604.20021)] the following result is obtained. Theorem: Let H be a finite, solvable group admitting an automorphism \(\alpha\) of prime order p. Suppose that \([H,\alpha]=H\) and let \(G=H<\alpha >\) be the semidirect product of H and \(<\alpha >\). If the order of every element in \(G\setminus H\) divides p.q where q is a prime different from p, then the Fitting length of H is at most 2.
Reviewer: I.Ş.Güloğlu

MSC:

20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D60 Arithmetic and combinatorial problems involving abstract finite groups
20D25 Special subgroups (Frattini, Fitting, etc.)
20D15 Finite nilpotent groups, \(p\)-groups
20D45 Automorphisms of abstract finite groups

Citations:

Zbl 0604.20021
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References:

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