SUBGROUPS IN FINITE QUASITHIN GROUPS

A finite group is called quasithin if for any 2-local subgroup in and any odd prime . As usual, denotes the -rank of the group . Let denote the set of all known (at the present time) finite non-abelian simple groups. A group is called a -group if each of its proper non-abelian simple sections belongs to . The current state of the classification of finite simple groups points to the importance of studying simple quasithin -groups . The structure of proper subgroups in such groups are investigated in this paper.Moreover, a detailed study is made of the structure of 2-local subgroups in quasithin -groups whose 2-local 3-rank does not exceed 1. As an example of how the results can be applied, we examine the component case of a problem concerning quasithin groups of 2-local 3-rank at most 1.Bibliography: 16 titles.