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Questions about the branch of algebra that deals with groups.

0 votes
1 answer
166 views

Automorphisms of nilpotent groups of class two

Is there any article that help me study automorphisms of nilpotent groups of class two with cyclic center? In "Odd order nilpotent groups of class two with cyclic centre, Y. K. Leong (1974)" there is …
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1 vote
1 answer
154 views

automorphisms of a finite $p$-group

If $G=\langle a, b : a^{p^{n}}= 1= b^{p^{n+1}}, [b, a]= b^{p} \rangle$, such that $n\geq 2$ and $p$ is an odd prime number, then how can I define a non-inner automorphism of $G$? Is it possible to f …
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  • 21
1 vote
0 answers
184 views

central automorphisms

‎Let ‎‎$‎‎C_{Aut_{c}(G)}(Z(G))$ ‎be ‎‎‎‎‎‎the group of all central automorphisms of finite non abelian $p$-group ‎$‎G‎$‎ fixing ‎$‎Z(G)‎$ element wise. If $‎‎C_{Aut_{c}(G)}(Z(G))$ is a proper subgroup …
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