On the automorphism groups of 2-generator 2-groups of class two

Subject Areas : Group theory

M.  Hashemi ¹ (Mathematics Faculty, University of Guilan, Rasht, Iran)
M.  Polkouei ² (Mathematics Faculty, University of Guilan, Rasht, Iran)

Received: 2020-03-25 Accepted : 2021-05-28 Published : 2021-06-01

Keywords: Automorphism groups, 2-groups, nilpotency class,

Abstract :

In this paper, by using the relations and properties of some classes of two generator2-groups of nilpotency class two, we find the order of automorphism group of these groups.

References:

[1] J. N. S. Bidwell, M. J. Curran, The automorphism group of a split metacyclic p-group, Arch. Math. 87 (6) (2006), 488-497.

[2] M. Hashemi, On the automorphism of some classes of groups, Ukrainian Math. J. 61 (12) (2009), 1995-2007.

[3] A. R. Jamali, Some new nonabelian 2-groups with abelian automorphism groups, J. Group Theory. 5 (1) (2002), 53-57.

[4] L. C. Kappe, N. Sarmin, M. Visscher, Two-generator 2-groups of class two and their nonabelian tensor squares, Glasgow Math. J. 41 (1999), 417-430.

[5] The GAP Group, GAP-Groups, Algorithms, and Programming, Version 4.4.12. (http://www. gap–system.org)