Characterization and axiomatization of all semigroups whose square is group

Document Type : Research Paper


Shiraz Branch, Islamic Azad University


In this paper we give a characterization for all semigroups whose square is a group. Moreover, we axiomatize such semigroups and study some relations between the class of these semigroups and Grouplikes,
introduced by the author. Also, we observe that this paper characterizes and axiomatizes a class of Homogroups (semigroups containing an ideal subgroup).  Finally, several equivalent conditions for a semigroup $S$ with $S^2\leq S$ (the square-group property) will be considered.


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