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The structure of EAP-groups and self-autopermutable subgroups.


ABSTRACT: A subgroup H of a given group G is said to be autopermutable, if HH(α) = H(α)H for all α ∈ Aut(G). We also call H a self-autopermutable subgroup of G, when HH(α) = H(α)H implies that H(α) = H. Moreover, G is said to be EAP-group, if every subgroup of G is autopermutable. One notes that if α runs over the inner automorphisms of the group, one obtains the notions of conjugate-permutability, self-conjugate-permutability, and ECP-groups, which were studied by Foguel in 1997, Li and Meng in 2007, and Xu and Zhang in 2005, respectively. In the present paper, we determine the structure of a finite EAP-group when its centre is of index 4 in G. We also show that self-autopermutability and characteristic properties are equivalent for nilpotent groups.

SUBMITTER: Housieni S 

PROVIDER: S-EPMC4276676 | biostudies-other | 2014

REPOSITORIES: biostudies-other

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