The articles [2], [3], [1], [4], and [5] provide the terminology and notation for this paper. For simplicity, we adopt the following rules: G denotes a group, A, B denote non empty subsets of G, N , H, H1, H2 denote subgroups of G, and x, a, b denote elements of G. Next we state a number of propositions: (1) For every normal subgroup N of G and for all elements x1, x2 of G holds x1 ·N · (x2 ·N)...

The present article is a summary of joint work of the author and Phillip Wesolek on the normal subgroup structure of totally disconnected locally compact second-countable (t.d.l.c.s.c.) groups. The general strategy is as follows: We obtain normal series for a t.d.l.c.s.c. group in which each factor is ‘small’ or a non-abelian chief factor; we show that up to a certain equivalence relation (call...

Abstract In this paper, it is shown that for a minimal system ( X , G ), if H normal subgroup of with finite index n then can be decomposed into components closed sets such each component under -action. Meanwhile, we prove residual set points in finitely many commuting homeomorphisms, the return times to any non-empty open contains arbitrarily long geometric progressions multidimension, extendi...

We study random walks on the Cremona group. show that almost surely dynamical degree of a sequence transformations grows exponentially fast, and walk produces infinitely many different normal subgroups with probability 1. Moreover, we structure such subgroups. prove these results in general for groups isometries (non-proper) hyperbolic spaces which possess at least one WPD element. As another a...

Introduction: Impaired wound healing in diabetic patients is a major clinical problem, which is associated with significant morbidity and mortality. Estrogen has positive effects on neoangiogenesis, reepithelialization and cell proliferation. In this research, effect of estrogen on wound healing in diabetic male rats was investigated. Methods: This study was performed on male Wistar rats (bo...

In this paper, the notion of the normal level sub HX group is introduced. We discuss the properties of normal level sub HX groups of a bipolar fuzzy normal HX subgroup of a HX group under homomorphism and anti-homomorphism. AMS Subject Classification (2000): 20N25, 03E72, 03F055, 06F35, 03G25. Keywordsfuzzy set, bipolar fuzzy set, bipolar fuzzy HX subgroup, bipolar fuzzy normal HX subgroup, lev...

When N is a normal subgroup of G, can we reconstruct G from N and G/N? In general, no. For instance, the groups Z/(p2) and Z/(p) × Z/(p) (for prime p) are nonisomorphic, but each has a cyclic subgroup of order p and the quotient by it also has order p. As another example, the nonisomorphic groups Z/(2p) and Dp (for odd prime p) have a normal subgroup that is cyclic of order p, whose quotient is...

Let S be a 2-group. The rank (normal rank) of S is the maximal dimension of an elementary abelian subgroup (a normal elementary abelian subgroup) of S over Z2. The purpose of this article is to determine the rank and normal rank of S, where S is a Sylow 2-subgroup of the classical groups of odd characteristic.

Let G be a connected reductive linear algebraic group. We use geometric methods to investigate G-completely reducible subgroups of G, giving new criteria for G-complete reducibility. We show that a subgroup of G is G-completely reducible if and only if it is strongly reductive in G; this allows us to use ideas of R.W. Richardson and Hilbert– Mumford–Kempf from geometric invariant theory. We ded...

To evaluate the impact of low levels of high density lipoprotein cholesterol (HDL-c) on patients with LDL-c average levels, focusing on oxidative, lipidic, and inflammatory profiles. Patients with cardiovascular risk factors (n = 169) and control subjects (n = 73) were divided into 2 subgroups, one of normal HDL-c and the other of low HDL-c levels. The following data was analyzed: BP, BMI, wais...