Class of Groups Close to Groups with the Basis Property
DOI:
https://doi.org/10.29020/nybg.ejpam.v19i2.7821Keywords:
Generalized Quaternion group, Generation, Basis Property.Abstract
Let G be a finite group. In [10, 11], Jones P. introduced and initiated the study of semigroups and groups with the Basis Property, after that Alkhalaf A. investigated the properties of semigroups and groups exhibiting the Basis Property. In our work, we aim to investigate whether certain classes of groups lack this property. Specifically, we demonstrate that the symmetric groups Sn for n > 3, cyclic groups of non-prime-power order, non-abelian simple groups, and groups constructed as extensions of a p-group P by a generalised quaternion group Q, do not possess the Basis Property.
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Copyright (c) 2026 Maram Alosaimi, Iman Taha, Ahmad Alkhalaf
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