CIT GROUPS OF FINITE MORLEY RANK .1.

[摘要] This is the first of two papers whose goal is the proof of the following result: THEOREM. Let G he an infinite omega-stable group of finite rank. Assume G has involutions and that the centralizer of any ivolution is a 2-group. Then one of the following holds: (1) G has a normal, nontrivial 2-subgroup. (2) G congruent-to H x S where H is a definable, abelian 2'-subgroup and S is a finite Sylow 2-subgroup of G with a unique involution that acts on H hy inversion. (3) G congruent-to SL2(K) for some algebraically closed field K of characteristic 2. In this paper, we show that if Case 1 fails and if the Sylow 2-subgroups are finite, then we are in the second case. We also show that when G has infinite disjoint Sylow 2-subgroups, then we are in Case 3. (C) 1994 Academic Press, Inc.

[发布日期] 1994-04-15