Glasnik matematički, Vol. 48 No. 1, 2013.
Izvorni znanstveni članak
https://doi.org/10.3336/gm.48.1.08
Commuting automorphisms of some finite groups
S. Fouladi
; Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani Ave., Tehran 1561836314 , Iran
R. Orfi
; Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
Sažetak
Let G be a group. An automorphism α of G is called a commuting automorphism if xxα=xα x for all x G. We denote the set of all commuting automorphisms of G by A(G). Moreover a group G is called an AC-group if the centralizer of every non-central element of G is abelian. In this paper we show that A(G) is a subgroup of the automorphism group of G for all finite AC-groups, p-groups of maximal class, and metacyclic p-groups.
Ključne riječi
Commuting automorphisms; AC-groups; minimal non-abelian p-groups; metacyclic p-groups; p-groups of maximal class
Hrčak ID:
103317
URI
Datum izdavanja:
4.6.2013.
Posjeta: 920 *