ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 00A, 26A Subbotin, Igor Ya., National University, USA Kurdachenko, Leonid A., Dnepropetrovsk University, Ukraine, On groups with many periodic factor-groups Let X be a class of groups. A group G is called a a just-non-X-group if G is not an X-group but all its proper factor-groups are X-groups. M. F. Newman described just-non-abelian groups. The study of just infinite groups was done by D. McCarthy, J. S. Wilson. J. R. Groves, and later D. J. S. Robinson and J. S. Wilson considered the soluble groups with polycyclic and supersoluble proper factor-groups. Groups with Chernikov proper factorgroups and just-non-FC-groups have been investigated by S. Franciosi, F. de Giovanni and L. A. Kurdachenko. S. Franciosi and F. de Giovanni also considered just-non-N_{c} groups. Just-non-CC-groups have been studied by L. A. Kurdachenko and J. Otal. The description of just non-hypercentral groups and just-non-hyperfinite groups is the subject of our talk.