IJPAM: Volume 93, No. 1 (2014)

ON CLASS PRESERVING AUTOMORPHISMS OF
SOME GROUPS OF ORDER $p^{6}$

Shiv Narain$^1$, Ram Karan$^2$
$^{1,2}$Department of Mathematics
Kurukshetra University
Kurukshetra, 136 119, INDIA


Abstract. For an odd prime $p$ there are 43 isoclinism families of groups of order $p^{6}$ given by James [#!James!#]. Let $G$ be a group lying in these families.

We sort out those groups for which $Aut_{c}(G)=Inn(G)$. Let $Autcent(G)$ denotes the groups of all central automorphisms of $G$. We give an upper bound for $\vert Aut_{c}(G)\vert$ in terms of $\vert Aut_{c}(G)\cap Autcent(G)\vert$ and $\vert Aut_{c}(G/Z(G)\vert$.

Received: August 20, 2013

AMS Subject Classification: 20D45, 20D15

Key Words and Phrases: finite p-groups, inner automorphism, class preserving automorphism, central automorphism, isoclinism

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DOI: 10.12732/ijpam.v93i1.2 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 1
Pages: 7 - 21

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).