Finite groups with its power automorphism groups having small indices

Generalized norms of groups: retrospective review and current status

“…The norm of a group was quite actively studied by R. Baer [2]- [11], as well as a number of authors [13,17,22,23,41,48,54,62,[109][110][111]119,121,[126][127][128]132].…”

“…The conditions of the norm to be Abelian [11], its relations with the center of a group [9,13,48,109,111,132], properties of groups, which norm has some index [127,128], as well as groups that have an Abelian or cyclic quotient group G/N (G) [5,8,126] are considered. In particular, in [126] it was proved that in a őnite group G the quotient group G/N (G) is cyclic if and only if a group G is nilpotent with cyclic quotient groups P/N (P ) for every Sylow subgroup P of a group G.…”