let $g$ be a finite group‎. ‎a subgroup‎ ‎$h$ of $g$ is called an $mathcal h $ -subgroup in‎ ‎$g$ if $n_g (h)cap h^gleq h$ for all $gin‎ ‎g$. a subgroup $h$ of $g$ is called a weakly‎ $mathcal h^ast $-subgroup in $g$ if there exists a‎ ‎subgroup $k$ of $g$ such that $g=hk$ and $hcap‎ ‎k$ is an $mathcal h$-subgroup in $g$. we‎ ‎investigate the structure of the finite group $g$ under the‎ ‎assump...

In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the s...

In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...

Let Mod(S) denote the mapping class group of a compact, orientable surface S. We prove that finitely generated subgroups of Mod(S) which are not virtually abelian have uniform exponential growth with minimal growth rate bounded below by a constant depending only on S.

I n r e s p o n s e : Regarding the subgroup analyses in ASCOT, as displayed in Figure 5 and Table 4 of the ASCOT-LLA paper (2), there were 7 subgroups in which a statistically significant beneficial effect of atorvastatin was not observed. However, as the authors noted and as was displayed visually in Figure 5, the proportional beneficial effect on 6 subgroups (diabetes, left ventricular hyper...

PURPOSE Cerebrovascular events (CVE) are the third most common cause of death in Western countries and about 65-70% of CVE are due to atherosclerotic disease of carotid arteries. Color Doppler scanning is used to evaluate the presence, severity and type of atheromatous plaques as well as velocity parameters of carotid arteries. We performed this study to correlate data of morphological and velo...

background: application of bonding agents (ba) into deep cavities and light curing them might increase pulpal temperature and threaten its health. the purpose of this study was to evaluate temperature rise of pulp by light curing six ba using two different light curing units (lcu), through a dent in wall of 0.5 mm. materials and methods: this in vitro experiment was carried out on 96 slices of ...

We develop methods for listing, for a given 2-group S, all nonconstrained centerfree saturated fusion systems over S. These are the saturated fusion systems which could, potentially, include minimal examples of exotic fusion systems: fusion systems not arising from any finite group. To test our methods, we carry out this program over four concrete examples: two of order 2 and two of order 2. Ou...

In this paper, the notions of   , q  -Q-fuzzy subgroup and normal subgroup are introduced and some of their properties are investigated.

The theory of fuzzy sets was inspired by Zadeh [10]. Subsequently, Rosenfeld introduced the concept of a fuzzy subgroup of a group [9]. Fuzzy cosets and fuzzy normal subgroups of a group G have been studied in [3, 5, 8]. In [4], the ring of cosets of a fuzzy ideal was constructed. Let A and B be fuzzy subgroups of G such that B ⊆ A. The purpose of this paper is to introduce the notion of fuzzy ...