On finite complete groups

Automorphisms of groups

“…All finite metabelian complete groups were determined by Gagen. The more general class of finite Abelian-by-nilpotent groups was considered by Gagen and Robinson (see [89]). …”

Minimal odd order automorphism groups

“…Several papers in the literature deal with the construction of complete groups of odd order (see [4], [6], [5], [11] and [14] for example), but the smallest possible order of such a group is unknown. The smallest example in the literature seems to be a complete group of order 3 12 Á 5 constructed in [6].…”

“…groups have attracted some attention, because of the surprising di‰culty in finding explicit examples of them. Though there are a number of results indicating that such groups are ubiquitous (for example, see [5], [7] and [9]), no simple search among 'small' groups will yield any examples. More precisely, MacHale and Sheehy [8] proved that there is no finite N.I.…”