Abstract The structure of locally soluble periodic groups in which every abelian subgroup is cyclic was described over 20 years ago. We complete the aforementioned characterization by dealing with non-periodic case. also describe finite all subgroups are cyclic.

A theorem by Zacher and Rips states that the finiteness of the index of a subgroup can be described in terms of purely lattice-theoretic concepts. On the other hand, it is clear that if G is a group and H is a subgroup of finite index of G, the index |G : H| cannot be recognized in the lattice L(G) of all subgroups of G, as for instance all groups of prime order have isomorphic subgroup lattice...

In this paper, we deal with Molaei’s generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set 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 (body ...

Let $G$ be a group and $Aut(G)$ be the group of automorphisms of‎ ‎$G$‎. ‎For any natural‎ number $m$‎, ‎the $m^{th}$-autocommutator subgroup of $G$ is defined‎ ‎as‎: ‎$$K_{m} (G)=langle[g,alpha_{1},ldots,alpha_{m}] |gin G‎,‎alpha_{1},ldots,alpha_{m}in Aut(G)rangle.$$‎ ‎In this paper‎, ‎we obtain the $m^{th}$-autocommutator subgroup of‎ ‎all finite abelian groups‎.

1. A considerable amount is known about the structure of finite factorizable groups—that is, groups G which can be represented in the form AB, where A and B are subgroups of G. Such groups are known to be solvable under a variety of assumptions on the subgroups A and B. If A and B are both Abelian, Ito [6] has shown that G is actually metabelian. If A and B are both cyclic, it is easy to see th...

‎In this study‎, ‎Frattini supplement subgroup and Frattini supplemented group‎ ‎are defined by Frattini subgroup‎. ‎By these definitions‎, ‎it's shown that‎ ‎finite abelian groups are Frattini supplemented and every conjugate of a‎ ‎Frattini supplement of a subgroup is also a Frattini supplement‎. ‎A group action‎ ‎of a group is defined over the set of Frattini supplements of a normal‎ ‎subgro...

The article studies the verb of sounding as one subgroup into incompletepersonal paradigm; extralinguistic and intralinguistic reasons active use ofsuch verbs predicatesare defined. characteristic two, three compound types two-membersentences’formalgrammatical structure is given, features morphological presentation subordinate partsof sentence are described.

In this paper we study the structure of locally solvable, solvable, locally nilpotent, and nilpotent maximal subgroups of skew linear groups. In [S. Akbari et al., J. Algebra 217 (1999) 422–433] it has been conjectured that if D is a division ring and M a nilpotent maximal subgroup of D∗, then D is commutative. In connection with this conjecture we show that if F [M]\F contains an algebraic ele...