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On the
Chermak–Delgado lattices of split metacyclic $p$-groups
Erin Brush, Jill Dietz, Kendra Johnson-Tesch and Brianne Power
Vol. 9 (2016), No. 5, 765–782
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Abstract |
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The Chermak–Delgado measure of a subgroup of a finite group is defined as . The subgroups with maximal Chermak–Delgado measure form a poset and corresponding lattice, known as the CD-lattice of . 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 -groups in particular. We also describe a rank-symmetric sublattice of the CD-lattice of split metacyclic -groups. |
Keywords
centrally large subgroups, Chermak–Delgado measure,
lattices of subgroups, metacyclic $p$-groups
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Mathematical Subject Classification 2010
Primary: 20D30
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Milestones
Received: 16 March 2015
Revised: 1 October 2015
Accepted: 27 October 2015
Published: 25 August 2016
Communicated by Kenneth S. Berenhaut
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Authors |
| Erin Brush | |
| St. Olaf College Northfield, MN 55057 United States |
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| Jill Dietz | |
| Department of Mathematics,
Statistics and Computer Science St Olaf College 1520 St. Olaf Avenue Northfield, MN 55057 United States |
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| Kendra Johnson-Tesch | |
| St. Olaf College Northfield, MN 55057 United States |
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| Brianne Power | |
| St. Olaf College Northfield, MN 55057 United States |
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