On the Structure of Locally Compact Topological Groups.
We classify the maximal irreducible periodic subgroups of PGL(q, ), where is a field of positive characteristic p transcendental over its prime subfield, q = p is prime, and × has an element of order q. That is, we construct a list of irreducible subgroups G of GL(q, ) containing the centre ×1q of GL(q, ), such that G/ ×1q is a maximal periodic subgroup of PGL(q, ), and if H is another group of this kind then H is GL(q, )-conjugate to a group in the list. We give criteria for determining...
We describe the finite groups satisfying one of the following conditions: all maximal subgroups permute with all subnormal subgroups, (2) all maximal subgroups and all Sylow -subgroups for permute with all subnormal subgroups.
In this paper, we give a generalization of Baer Theorem on the injective property of divisible abelian groups. As consequences of the obtained result we find a sufficient condition for a group to express as semi-direct product of a divisible subgroup and some subgroup . We also apply the main Theorem to the -groups with center of index , for some prime . For these groups we compute the number of conjugacy classes and the number of abelian maximal subgroups and the number of nonabelian...