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Publicly Available Published by De Gruyter October 2, 2013

Groups whose Chermak–Delgado lattice is a chain

  • Ben Brewster EMAIL logo , Peter Hauck and Elizabeth Wilcox
From the journal Journal of Group Theory

Abstract.

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.

Funding source: Colgate University Faculty Research Council

Received: 2013-05-12
Published Online: 2013-10-02
Published in Print: 2014-03-01

© 2014 by Walter de Gruyter Berlin/Boston

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