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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

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

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Volume 17, Issue 2


Groups whose Chermak–Delgado lattice is a chain

Ben Brewster / Peter Hauck / Elizabeth Wilcox
Published Online: 2013-10-02 | DOI: https://doi.org/10.1515/jgt-2013-0043


For a finite group G with subgroup H, the Chermak–Delgado measure of H in G refers to |H||CG(H)|. The set of all subgroups with maximal Chermak–Delgado measure form a sublattice, 𝒞𝒟(G), within the subgroup lattice of G. This paper examines conditions under which the Chermak–Delgado lattice is a chain of subgroups H0<H1<<Hn. On the basis of a general result about extending certain Chermak–Delgado lattices, we construct, for any prime p and any non-negative integer n, a p-group whose Chermak–Delgado lattice is a chain of length n.

About the article

Received: 2013-05-12

Published Online: 2013-10-02

Published in Print: 2014-03-01

Citation Information: Journal of Group Theory, Volume 17, Issue 2, Pages 253–265, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt-2013-0043.

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