非次正规的非交换的非TI-子群的个数不超过21的非可解群

On Non-Solvable Groups Having at Most 21 Non-Subnormal Non-Abelian Non-TI-Subgroups

为了进一步研究非TI-子群的个数对有限群可解性的影响,先考察非交换的非TI?子群,证明了如果非可解群G的非交换的非TI?子群的个数不超过21,则G同构于交错群A5。进而考察非次正规的非交换的非TI-子群的个数,证明了如果非可解群G的非次正规的非交换的非TI?子群的个数不超过21,则亦有G同构于A5。

In order to give a further study of the influence of the number of non-TI-subgroups on the solvability of fi-nite groups,we first investigate non-abelian non-TI-subgroups and prove that if G is a non-solvable group having at most 21 non-abelian non-TI-subgroups,G is isomorphic to the alternating group A5.Moreover,we investigate non-subnormal non-abelian non-TI-subgroups and we also have that G is isomorphic to A5 if G is a non-solvable group having at most 21 non-subnormal non-abelian non-TI-subgroups.