IJPAM: Volume 81, No. 3 (2012)

SOME NEW NON-ABELIAN $2$-GROUPS $G$ WITH
EVERY AUTOMORPHISM FIXING $G/\Phi(G)$ ELEMENTWISE

Rasoul Soleimani
Department of Mathematics
Payame Noor University
P.O. Box 19395-3697, Tehran, IRAN


Abstract. In this paper, we exhibit an infinite family of non-abelian $2$-groups $G$ in which each automorphism fix $G/\Phi(G)$ elementwise.

Received: October 6, 2012

AMS Subject Classification: 20D45, 20D15, 20D25

Key Words and Phrases: automorphism, $2$-group, Frattini subgroup

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 3