A note on a characterization of generalized quaternion 2-groups

Yanheng Chen; Guiyun Chen

doi:10.1016/j.crma.2014.04.009

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A note on a characterization of generalized quaternion 2-groups

Yanheng Chen Guiyun Chen

Year: 2014 Journal: Comptes Rendus Mathématique Vol: 352 (6)Pages: 459-461 Publisher: Elsevier BV

DOI: 10.1016/j.crma.2014.04.009

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Abstract

In this note, we answer an open problem posed in M. Tărnăceanu (2010) [5], and obtain that the generalized quaternion 2-groups are the unique finite noncyclic groups whose posets of conjugacy classes of cyclic subgroups have breaking points.

Keywords:

Quaternion Conjugacy class Mathematics Point (geometry) Group (periodic table) Combinatorics Characterization (materials science) Pure mathematics Algebra over a field Physics Geometry Quantum mechanics

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Finite Group Theory Research

Physical Sciences → Mathematics → Discrete Mathematics and Combinatorics

Geometric and Algebraic Topology

Physical Sciences → Mathematics → Geometry and Topology

Graph theory and applications

Physical Sciences → Mathematics → Geometry and Topology

A note on a characterization of generalized quaternion 2-groups

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