Involve: A Journal of Mathematics

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

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

Erin Brush, Jill Dietz, Kendra Johnson-Tesch, and Brianne Power

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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
Received: 16 March 2015
Revised: 1 October 2015
Accepted: 27 October 2015
First available in Project Euclid: 22 November 2017

Permanent link to this document
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

Keywords
centrally large subgroups Chermak–Delgado measure lattices of subgroups metacyclic $p$-groups

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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