In this paper we define a new monoid construction under crossed products for given monoids. We also present a generating set and a relator set for this product. Finally, we give the necessary and sufficient conditions for the regularity of it. MSC: 05C10; 05C12; 05C25; 20E22; 20M05
In this paper, we generalize some results related to the congruence subgroups of modular group ; given in [7] and [6] by Kiming, Schütt, and Verrill, to the extended modular group :
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