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Abstract
This paper gives a characterization of finite groups G in which each cyclic subgroup either is normal in G or normalizes all subgroups of G.
sequences over finite abelian p -groups Rocky Mt. J. Math. 37 1541 – 1550 10.1216/rmjm/1194275933 . [10] Gao , W. , Geroldinger , A. , Schmid , W. A. 2007 Inverse zero-sum problems Acta
Abstract
In this paper we analyse the natural permutation module of an affine permutation group. For this the regular module of an elementary Abelian p-group is described in detail. We consider the inequivalent permutation modules coming from nonconjugate complements. We prove their strong structural similarity well exceeding the fact that they have equal Brauer characters.
Abstract
Let G be a finite group. For a finite p-group P the subgroup generated by all elements of order p is denoted by Ω1(p). Zhang [5] proved that if P is a Sylow p-subgroup of G, Ω1(P) ≦ Z(P) and N G (Z(P)) has a normal p-complement, then G has a normal p-complement. The object of this paper is to generalize this result.
Summary
A group is called equilibratedif no subgroup Hof Gcan be written as a product of two non-normal subgroups of H. Blackburn, Deaconescu and Mann [1] investigated the finite equilibrated groups, giving a complete description of the non-soluble ones. On the other hand, they showed that the property of a finite nilpotent group of being equilibrated depends solely on the structure of its 2-generated p-subgroups. Consequently, all the finite 2-generated equilibrated p-groups were classified for any odd prime p,but the case p=2 remained unsolved. This special case will represent the subject of the present paper.
An abelian p-group G has a nice basis if it is the ascending union of a sequence of nice subgroups, each of which is a direct sum of cyclic groups. It is shown that if G is any group, then G ⊕ D has a nice basis, where D is the divisible hull of p ω G. This leads to a consideration of the nice basis rank of G, i.e., the smallest rank of a divisible group D such that G ⊕ D has a nice basis. This concept is used to show that there exist a reduced group G and a non-reduced group H, both without a nice basis, such that G ⊕ H has a nice basis
The aim of this study was to investigate the effect of estradiol and progesterone and melatonin supplementation on TNF-a levels in ovariectomized and pinealectomized rats. The study was carried out on 42 adult, Spraque-Dawley strain female rats aged 6 months and weighing 200-250 grams. The rats were divided into 6 groups, each group contained 7 rats. Group 1: Sham-ovariectomized (Sham-Ovx), Group 2: Ovariectomized (Ovx), Group 3: Ovx and estradiol (E) and progesterone (P) supplemented (Ovx+E-P) group, Group 4: Ovx+E-P+Melatonin (M) supplemented group, Group 5: Ovx - Pinealectomized (Pnx) group, Group 6: Ovx - Pnx+E-P supplemented group. Serum TNF-a levels were determined after 4 weeks application period. Group 6 (Ovx-Pnx+E-P) has the highest serum TNF-a compared with other groups while group 2 (ovariectomized), has the lowest levels (P<0.001). Group 5 was higher than groups 1, 2, 3 and 4 (P<0.001). The results of the study show that ovariectomy reduces the serum level of TNF-a, but estradiol and progesterone application prevents this reduction in ovariectomized rats. However, pinealectomy intensifies the increases in TNF- a levels in ovariectomized and estradiol and progesterone supplemented rats, whereas melatonin reduces TNF- a levels in ovariectomized rats.
The objective of this study was to determine whether creatine supplementation (CrS) could improve mechanical power output, and swimming performance in highly trained junior competitive fin swimmers. Sixteen male fin swimmers (age:15.9±1.6 years) were randomly and evenly assigned to either a creatine (CR, 4×5 g/day creatine monohydrate for 5 days) or placebo group (P, same dose of a dextrose-ascorbic acid placebo) in a double-blind research. Before and after CrS the average power output was determined by a Bosco-test and the swimming time was measured in two maximal 100 m fin swims. After five days of CrS the average power of one minute continuous rebound jumps increased by 20.2%. The lactate concentration was significantly less after 5 minutes restitution at the second measurement in both groups. The swimming time was significantly reduced in both first (pre: 50.69±1.41 s; post: 48.86±1.34 s) and second (pre: 50.39±1.38 s; post: 48.53±1.35 s) sessions of swimming in CR group, but remained almost unchanged in the P group.The results of this study indicate that five day Cr supplementation enhances the dynamic strength and may increase anaerobic metabolism in the lower extremity muscles, and improves performance in consecutive maximal swims in highly trained adolescent fin swimmers.
