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- Type of Document: Article
- DOI: 10.1080/00927872.2016.1175587
- Publisher: Taylor and Francis Inc , 2017
- Abstract:
- In this paper, we define the concept of integral for an arbitrary group, and we try to answer this question: Which groups can be considered as a commutator subgroup? For instance, we will show that symmetric group Sn for n ≥ 3, generalized quaternion group Q2n for n ≥ 4 and Dihedral group Dn for n ≥ 3 cannot occur as commutator subgroup of any group. Moreover, we characterize all finite groups with the cyclic commutator subgroup isomorphic to Z2n or Z3n.© 2017, Copyright © Taylor & Francis Group, LLC
- Keywords:
- Automorphism group ; Central product ; Characteristic subgroup ; p-groups ; Semidirect product ; Symmetric groups
- Source: Communications in Algebra ; Volume 45, Issue 3 , 2017 , Pages 1105-1113 ; 00927872 (ISSN)
- URL: https://www.tandfonline.com/doi/abs/10.1080/00927872.2016.1175587?journalCode=lagb20