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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

6 Issues per year


IMPACT FACTOR 2017: 0.581

CiteScore 2017: 0.53

SCImago Journal Rank (SJR) 2017: 0.778
Source Normalized Impact per Paper (SNIP) 2017: 0.893

Mathematical Citation Quotient (MCQ) 2017: 0.45

Online
ISSN
1435-4446
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Volume 13, Issue 6

Issues

The power graph of a finite group, II

Peter J. Cameron
  • School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, U.K. E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2010-05-30 | DOI: https://doi.org/10.1515/jgt.2010.023

Abstract

The directed power graph of a group G is the digraph with vertex set G, having an arc from y to x whenever x is a power of y; the undirected power graph has an edge joining x and y whenever one is a power of the other. We show that, for a finite group, the undirected power graph determines the directed power graph up to isomorphism. As a consequence, two finite groups which have isomorphic undirected power graphs have the same number of elements of each order.

About the article

Received: 2010-01-04

Published Online: 2010-05-30

Published in Print: 2010-11-01


Citation Information: Journal of Group Theory, Volume 13, Issue 6, Pages 779–783, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt.2010.023.

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