Proceedings of the Japan Academy, Series A, Mathematical Sciences

On automorphisms of some $p$-groups

Manoj Kumar and Lekh Raj Vermani

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Abstract

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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 4 (2002), 46-50.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148392731

Digital Object Identifier
doi:10.3792/pjaa.78.46

Mathematical Reviews number (MathSciNet)
MR1900023

Zentralblatt MATH identifier
1062.20021

Subjects
Primary: 20D45: Automorphisms 20D15: Nilpotent groups, $p$-groups

Keywords
Cocycle coboundary inner automorphism conjugacy preserving automorphism Hasse principle

Citation

Kumar, Manoj; Vermani, Lekh Raj. On automorphisms of some $p$-groups. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 4, 46--50. doi:10.3792/pjaa.78.46. https://projecteuclid.org/euclid.pja/1148392731


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