Presentation of semidirect product of monogenic semigroups
Narges Hosseinzadeh, H. Doostie · International Mathematical Forum · 2013
By studying the semigroup presented by π = � A, B | A n+1 = A, B m+1 = B, BA = A n−1 B, B m = A n � , for every positive integers m, n ≥ 3 we show that, for even values of m this is an appropriate presentation for the semidirect product of monogenic semigroup S = � a | a n+1 = aby the monogenic semigroup T = � b | b m+1 = b� . Moreover, for odd values of m it is a commutative semigroup of order (3+(−1) n )m 2 . The interests of presentability of prod- ucts of semigroups are quite useful in the study of more effective and intrinsic properties of the products (like as the computation of their characters and studying their Green J-classes). Our method of proof based on using the theoretic definitions and hereby we will deduced the presentation of the direct product of monogenic semigroups for every integers n, m ≥ 3. Mathematics Subject Classification: 20M30, 20E45