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- Title
On equality of coset preserving subcentral automorphisms.
- Authors
Seifizadeh, Parisa; Farokhniaee, AmirAli
- Abstract
Let G be a finite non-abelian p-group, where p is a prime and M and N are two subcentral characteristic subgroups of G. An automorphism α of G is called subcentral automorphism if, for all g ∈ G, g-1α(g) ∈ M and for all n ∈ N, n-1α(n) = 1. Let AutMN (G), CAutMN(G) (Z(G)) and AutG'N (G) denote, respectively, the group of all subcentral automorphisms of G, the group of all subcentral automorphisms of G fixing the center of G, elementwise, and the group of all derival automorphisms of G fixing the elements of N. In this study, we present necessary and sufficient conditions on a finite p-group, G, such that AutMN (G) = CAutMN(G)(Z(G)) and AutMN (G) = AutG'N (G). Moreover, we investigate the necessary and sufficient conditions for the equality of inner automorphisms and the group of subcentral automorphisms that fix the center and the Frattini subgroup of, G, element wise.
- Subjects
MATHEMATICAL research; AUTOMORPHISMS; FRATTINI subgroups; MAXIMAL subgroups; ABELIAN p-groups
- Publication
Analele Ştiinţifice ale Universităţii 'Al.I. Cuza' din Iaşi. Matematică, 2023, Vol 69, Issue 1, p17
- ISSN
1221-8421
- Publication type
Article
- DOI
10.47743/anstim.2023.00002