Il gruppo degli automorfismi esterni di un -gruppo nilpotente infinito e suoi -sottogruppi normali
Inert subgroups of uncountable locally finite groups
Let be an uncountable universal locally finite group. We study subgroups such that for every , .
Infinite dimensional linear groups with many G - invariant subspaces
Let F be a field, A be a vector space over F, GL(F, A) be the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dim F(B/Core G(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char F.
Infinite locally finite groups of type PSL(2,K) or Sz(K) are not minimal under certain conditions.
In classifying certain infinite groups under minimal conditions it is needed to find non-simplicity criteria for the groups under consideration. We obtain some of such criteria as a consequence of the main result of the paper and the classification of finite simple groups.