ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 20, 05, 11 Shi, Wujie, Southwest Normal University, P. R. China A new classification of groups For any group G, denote by π_{e}(G) the set of all element orders in G. Given a group G, let h(π_{e}(G)) be the number of isomorphism classes of groups with the same set π_{e}(G) of element orders. In terms of the function h , groups G are classified as follows : irrecognizable groups if h(π_{e}(G)) = ∞; otherwise G is called recognizable groups. A recognizable group G is called a k-recognizable group if h(π_{e}(G)) = k. Usually, an 1-recognizable group is called a characterizable group. We prove that many finite simple groups(e. g. sporadic groups except J_{2}) are characterizable, the groups which have a normal elementary abelian subgroup are irrecognizable and do not find k-recognizable group for k ≥ 3.