‎In this paper we prove that a finite group $G$ having at most three‎ ‎conjugacy classes of non-normal non-abelian proper subgroups is‎ ‎always solvable except for $Gcong{rm{A_5}}$‎, ‎which extends Theorem 3.3‎ ‎in [Some sufficient conditions on the number of‎ ‎non-abelian subgroups of a finite group to be solvable‎, ‎Acta Math‎. ‎Sinica (English Series) 27 (2011) 891--896.]‎. ‎Moreover‎, ‎we s...

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 ...

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...

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 (body ...

‎let $g$ be a finite group and $nu(g)$ denote the number of conjugacy classes of non-normal subgroups of $g$‎. ‎in this paper‎, ‎all nilpotent groups $g$ with $nu(g)=3$ are classified‎.

We present a method of producing normal subgroups of the free group on r generators not containing a given word. Special attention is given to the normal subgroups of the free group on two generators. In considering the exponent sum of the generators in a given word, we produce such subgroups and clearly state for what class of words these subgroups are not easily obtainable. We also provide a ...

Now that the classification of finite simple groups is complete, it is logical to look at the extension problem. An important special case to consider is when M is a minimal normal subgroup of G and both G/M and M are known groups. If M is abelian, various techniques have been used to derive information about G. Indeed, almost the entire theory of finite solvable groups can be said to rest upon...

Our goal will be to generalize the construction of the group Z/nZ. The idea there was to start with the group Z and the subgroup nZ = 〈n〉, where n ∈ N, and to construct a set Z/nZ which then turned out to be a group (under addition) as well. (There are two binary operations + and · on Z, but Z is just a group under addition. Thus, the fact that we can also define multiplication on Z/nZ will not...