ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 20 Tavgeń, Oleg, Mateiko, Oleg, Belorussian State University, Belarus The free product of cyclic groups in the group PSL_{2}(ℂ). To classify linear representations of the group GL_{2}(ℤ), the authors studied in [1] representations of the free product of two cyclic groups in the group PSL_{2}(ℂ). In this report we consider families of faithful representations of the free product of n (n ≥ 2) cyclic groups in the group PSL_{2}(ℂ). The results are applied in the theory of one-relator products of cyclics. In particular, we generalize the result of Ree and Mendelsohn about free subgroups of a two generator one-relator group for the case of a n-generator (n ≥ 2) one-relator group. Reference: O. M. Mateiko and O. I. Tavgeń, Linear representations of the automorphism groups of the free groups, Topics in algebra, Gomel, 11(1997), 48–59.