Open Access
April 2002 On automorphisms of some $p$-groups
Manoj Kumar, Lekh Raj Vermani
Proc. Japan Acad. Ser. A Math. Sci. 78(4): 46-50 (April 2002). DOI: 10.3792/pjaa.78.46


A group $G$ is said to enjoy ``Hasse principle'' if every local coboundary of $G$ is a global coboundary. Let $G$ be a non-Abelian finite $p$-group of order $p^m$, $p$ prime and $m > 4$ having a normal cyclic subgroup of order $p^{m-2}$ but having no element of order $p^{m-1}$. We prove that $G$ enjoys ``Hasse principle'' if $p$ is odd but in the case $p = 2$, there are fourteen such groups twelve of which enjoy ``Hasse principle'' but the remaining two do not satisfy ``Hasse principle''. We also find all the conjugacy preserving outer automorphisms for these two groups.


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Manoj Kumar. Lekh Raj Vermani. "On automorphisms of some $p$-groups." Proc. Japan Acad. Ser. A Math. Sci. 78 (4) 46 - 50, April 2002.


Published: April 2002
First available in Project Euclid: 23 May 2006

zbMATH: 1062.20021
MathSciNet: MR1900023
Digital Object Identifier: 10.3792/pjaa.78.46

Primary: 20D15 , 20D45

Keywords: coboundary , Cocycle , conjugacy preserving automorphism , Hasse principle , inner automorphism

Rights: Copyright © 2002 The Japan Academy

Vol.78 • No. 4 • April 2002
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