Specific automorphisms on a 2-generated p-group of class two

Abstract

Let ‫ܩ‬ be a finite two generated ‫-‬group of nilpotency class two, where ‫‬ is a prime number. If ߶ሺ‫ܩ‬ሻ is the Frattini subgroup of ‫,ܩ‬ then ‫ܩ‬ ߶ሺ‫ܩ‬ሻ Τ is a vector space of dimension two over the field Ժ ‫‬Ժ Τ . In this paper, we determine those automorphisms on ‫ܩ‬ which induce identity transformation on ‫ܩ‬ ߶ሺ‫ܩ‬ሻ Τ . We use the most updated classification given for ‫ܩ‬ to find these automorphisms. The results of this study are applicable in classifying ‫,‪ሻ‬ܩ‪ሺ‬ݐݑܣ‬ the automorphism group of ‫.ܩ‬

On the autocentralizer subgroups of finite –groups

“…In this section we study the finite nonabelian p-groups, G, with |Cent(G)| = p + 2, and find bounds of the |Acent(G)|. In [8] two techniques were provided to find the automorphisms of G . We use these techniques, where G is a 2 -generated p -group of nilpotency class two.…”