COMMUTING AUTOMORPHISM OF p-GROUPS WITH CYCLIC MAXIMAL SUBGROUPS

Title & Authors
COMMUTING AUTOMORPHISM OF p-GROUPS WITH CYCLIC MAXIMAL SUBGROUPS
Vosooghpour, Fatemeh; Kargarian, Zeinab; Akhavan-Malayeri, Mehri;

Abstract
Let G be a group and let $\small{p}$ be a prime number. If the set $\small{\mathcal{A}(G)}$ of all commuting automorphisms of G forms a subgroup of Aut(G), then G is called $\small{\mathcal{A}(G)}$-group. In this paper we show that any $\small{p}$-group with cyclic maximal subgroup is an $\small{\mathcal{A}(G)}$-group. We also find the structure of the group $\small{\mathcal{A}(G)}$ and we show that $\mathcal{A}(G) Keywords commuting automorphism;cyclic maximal subgroup; Language English Cited by References 1. M. Deaconescu, Gh. Silberberg, and G. L. Walls, On commuting automorphisms of groups, Arch. Math. (Basel) 79 (2002), no. 6, 423-429. 2. M. Deaconescu and G. L. Walls, Right 2-Engel elements and commuting automorphism of group, J. Algebra 238 (2001), no. 2, 479-484. 3. D. S. Dummit and R. M. Foote, Abstract Algebra, Prentice-Hall, Inc, 1991. 4. I. N. Herstein, T. J. Laffey, Problems and solutions: Solutions of elementary problems: E3039, Amer. Math. Monthly 93 (1986), no. 10, 816-817. 5. Z. Kargarian and M. Akhavan Malayeri, On the commuting automrphisms of groups of order$p^3\$, Adv. Appl. Math. Sci. 9 (2011), no. 2, 115-120.

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