Finite groups with at most six subgroups not in the Chermak-Delgado lattice

Guojie Liu; Qiangwei Song; Guojie Liu; Qiangwei Song

doi:10.3934/era.2025256

Electronic Research Archive

2025, Volume 33, Issue 9: 5769-5775. doi: 10.3934/era.2025256

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Research article

Finite groups with at most six subgroups not in the Chermak-Delgado lattice

Guojie Liu ,
Qiangwei Song ^,

School of Mathematical Sciences, Shanxi Normal University, Taiyuan 030031, China

Received: 05 August 2025 Revised: 15 September 2025 Accepted: 18 September 2025 Published: 25 September 2025

The Chermak-Delgado lattice of a finite group $ G $ is a self-dual sublattice of the subgroup lattice of $ G $. In this paper, we determine finite groups with at most six subgroups not in the Chermak-Delgado lattice.
- Chermak-Delgado lattice,
- subgroup lattice,
- finite groups,
- finite solvable groups,
- Sylow subgroups
Citation: Guojie Liu, Qiangwei Song. Finite groups with at most six subgroups not in the Chermak-Delgado lattice[J]. Electronic Research Archive, 2025, 33(9): 5769-5775. doi: 10.3934/era.2025256

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Abstract

The Chermak-Delgado lattice of a finite group $ G $ is a self-dual sublattice of the subgroup lattice of $ G $. In this paper, we determine finite groups with at most six subgroups not in the Chermak-Delgado lattice.

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