Conditions, under which projective Sylow subgroups of almost locally normal group are locally conjugate

Abstract

Two subclasses of expansions of locally normal groups with the help of finite p-groups are selected, at which projective Sylow p-subgroups are locally conjugate. The subgroup F of a finite index contains in the first case invariant Sylow p-subgroup, in the second case Sylow p-subgroups in F are almost abelian. The example that is given shows that for both subclasses the condition of expansion of locally normal group with the help of just p-group is essential.