ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 20 Olga Macedońska, Silesian Technical University On semigroup identities in groups Let F be a free semigroup generated by x, y, . . .. A semigroup identity of a group G is a nontrivial identity of the form u = v where u, v ∈ F, which holds under every substitution of generators by elements from G. We discuss several open problems concerning semigroup identities and describe a wide class of groups in which: a group satisfies a semigroup identity if and only if it is an extention of a nilpotent group by a group of finite exponent.

Reference: Robert G. Burns, Olga Macedońska, and Yuri Medvedev, Groups Satisfying Semigroup Laws, and Nilpotent-by-Burnside Varieties, J. Algebra 195 (1997), 510-525 .