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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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1435-4446
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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

## Abstract.

For a finite group G with subgroup H, the Chermak–Delgado measure of H in G refers to $|H|\phantom{\rule{0.166667em}{0ex}}|{C}_{G}\left(H\right)|$. The set of all subgroups with maximal Chermak–Delgado measure form a sublattice, $\mathrm{𝒞𝒟}\left(G\right)$, within the subgroup lattice of G. This paper examines conditions under which the Chermak–Delgado lattice is a chain of subgroups ${H}_{0}<{H}_{1}<\cdots <{H}_{n}$. 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.

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,

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© 2014 by Walter de Gruyter Berlin/Boston.

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