ON SOME FINITENESS CONDITIONS IN SEMIGROUP AND GROUP-THEORY

In this paper we give answers to some questions stated by Shevrin [12] (see also Question 1.18 [71, Questions 51-56 [141) on dependences between some finiteness conditions such as the maximal and minimal conditions, finiteness of rank, finiteness of length and breadth. In Section 1 we recall the definitions and the questions, mention related facts and results. Section 2 is the proof of main Theorem 1. In Section 3 the groups from Theorems 2, 3, and 4 (on the basis of which Theorem 1 is proved) are constructed by means of defining relations.