Some Groups with Computable Chermak-Delgado Lattices

Ben Brewster; Elizabeth Wilcox

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arXiv · 1202.2385

Some Groups with Computable Chermak-Delgado Lattices

Ben Brewster·Elizabeth Wilcox

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Abstract

Let G be a finite group and let H be a subgroup of G. The Chermak-Delgado measure of H with respect to G is the product of the order of H with the order of the centralizer of H. Originally described by A. Chermak and A. Delgado, the collection of all subgroups of G with maximal Chermak-Delgado measure, denoted CD(G), is a sublattice of the lattice of all subgroups of G. In this paper we note that the members of CD(G) are subnormal in G and determine the Chermak-Delgado lattice of direct products. We additionally describe the lattice for certain kinds of wreath products and examine the behavior of centrally large subgroups, a subset of the Chermak-Delgado lattice.

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Ben Brewster, Elizabeth Wilcox. 2012-02-10. Some Groups with Computable Chermak-Delgado Lattices. https://arxiv.org/abs/1202.2385

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