## Involve: A Journal of Mathematics

• Involve
• Volume 9, Number 5 (2016), 765-782.

### On the Chermak–Delgado lattices of split metacyclic $p$-groups

#### Abstract

The Chermak–Delgado measure of a subgroup $H$ of a finite group $G$ is defined as $mG(H) = |H||CG(H)|$. The subgroups with maximal Chermak–Delgado measure form a poset and corresponding lattice, known as the CD-lattice of $G$. We describe the symmetric nature of CD-lattices in general, and use information about centrally large subgroups to determine the CD-lattices of split metacyclic $p$-groups in particular. We also describe a rank-symmetric sublattice of the CD-lattice of split metacyclic $p$-groups.

#### Article information

Source
Involve, Volume 9, Number 5 (2016), 765-782.

Dates
Revised: 1 October 2015
Accepted: 27 October 2015
First available in Project Euclid: 22 November 2017

https://projecteuclid.org/euclid.involve/1511371068

Digital Object Identifier
doi:10.2140/involve.2016.9.765

Mathematical Reviews number (MathSciNet)
MR3541978

Zentralblatt MATH identifier
1348.20023

Subjects
Primary: 20D30: Series and lattices of subgroups

#### Citation

Brush, Erin; Dietz, Jill; Johnson-Tesch, Kendra; Power, Brianne. On the Chermak–Delgado lattices of split metacyclic $p$-groups. Involve 9 (2016), no. 5, 765--782. doi:10.2140/involve.2016.9.765. https://projecteuclid.org/euclid.involve/1511371068

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