Maximal Groups in Free Burnside Semigroups

摘要: We prove that any maximal group in the free Burnside semigroup defined by equation x n =x n+m for ≥ 1 and m is a satisfying =1. show such over well described set of generators whose cardinality cyclomatic number graph associated to ℑ-class containing group. For n=2 every 2 we present examples with 2m−1 generators. Hence, these cases, have infinite groups large enough m. This allows us important properties semigroups case n=2, which was almost completely unknown until now. Surprisingly, presents simultaneously complexities cases n=1 3: are cyclic order 3 but they can more be ≤ 2; there exactly 2¦A¦ ℑ-classes easily characterized infinitely many, difficult characterize 2.