Let σ = {σi|i ∈ I } be a partition of the set all primes ℙ and G finite group. A ℋ subgroups is said to complete Hall σ-set if every member ≠1 σi-subgroup for some i contains exactly one such that σi ⌒ π(G) ≠ ∅. group σ-primary it σi-group i. subgroup be: σ-permutable in possesses AH x H xA G; σ-subnormal there chain A0 ≤ A1 … At either Ai − 1 ⊴ or /(Ai 1)Ai 1, …, t;

Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...

A transitively normal subgroup of a group G is one that is normal in every subgroup in which it is subnormal. This concept is obviously related to the transitivity of normality because the latter holds in every subgroup of a group G if and only if every subgroup of G is transitively normal. In this paper we describe the structure of a group whose cyclic subgroups (or a part of them) are transit...

The generalised Fitting subgroup of a finite group is the group generated by all subnormal subgroups that are either nilpotent or quasisimple. The importance of this subgroup in finite group theory stems from the fact that it always contains its own centraliser, so that any finite group is an abelian extension of a group of automorphisms of its generalised Fitting subgroup. We define a class of...

Let K[G] be the group algebra of a locally finite group G over a field K of characteristic p > 0. In this paper, we show that K[G] is semiprimitive if and only if G has no locally subnormal subgroup of order divisible by p. Thus we settle the semiprimitivity problem for such group algebras by verifying a conjecture which dates back to the middle 1970’s. Of course, if G has a locally subnormal s...

serum concentration of fsh, lh, testosterone, prolactin, acth, cortisol, tsh, t4, t3 and resin t3 uptake were measured in 146 men who were exposed to vesicants used by the iraqi regime a few days t04 weeks prior to testing. clinical and laboratory findings had confirmed the use of mustard gas. mean serum concentrations of fsh, lh, tsh and prolactin were not significantly different from normal v...

Abstract. This paper deals with combinatorial aspects of finite covers of groups by cosets or subgroups. Let a1G1, . . . , akGk be left cosets in a group G such that {aiGi} k i=1 covers each element of G at least m times but none of its proper subsystems does. We show that if G is cyclic, or G is finite and G1, . . . , Gk are normal Hall subgroups of G, then the inequality k > m + f([G : ⋂ k i=...