Growth sequences of finite semigroups

Journal of the Australian Mathematical Society

James Wiegold¹ 

[1] H. Lausch

关键词: 20 M 99;   

DOI  :  10.1017/S1446788700028925

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

The growth sequence of a finite semigroup S is the sequence {d(Sn)}, where Sn is the nth direct power of S and d stands for minimum generating number. When S has an identity, d(Sn) = d(Tn) + kn for all n, where T is the group of units and k is the minimum number of generators of S mod T. Thus d(Sn) is essentially known since d(Tn) is (see reference 4), and indeed d(Sn) is then eventually piecewise linear. On the other hand, if S has no identity, there exists a real number c > 1 such that d(Sn) ≥ cn for all n ≥ 2.

【 授权许可】

Unknown