We prove that a space is quotient π-image of a locally separable metric space if and only if it has a πand double cs∗cover. We also investigate quotient π-s-images of locally separable metric spaces.

In this paper, we introduce the notion of double-framed fuzzy quotient lattice in a fuzzy lattice and then some basic properties are investigated. Characterizations of double-framed fuzzy quotient lattices are given. Using a collection of lattices, a double framed fuzzy quotient lattice is established. The notion of fuzzy quotient lattice relation on the family of all I double-framed fuzzy sub ...

We show that the least genus of any compact Riemann surface S, admitting a simple Suzuki group G = Sz(^) as a group of automorphisms, is equal to 1 +|G|/40. We compute the number of such surfaces S as the number of normal subgroups of the triangle group A(2,4,5) with quotient-group G, and investigate the associated regular maps of type {4,5}.

We introduce a misere quotient semigroup construction in impartial combinatorial game theory, and argue that it is the long-sought natural generalization of the normal-play Sprague-Grundy theory to misere play. Along the way, we illustrate how to use the theory to describe complete analyses of two wild taking and breaking games.

Azad [1] introduced the concepts of fuzzy semi-open sets and fuzzy semi-continuous mappings. Fuzzy α-open sets and fuzzy α-continuous functions were introduced by Mashhour et. al. [4] and Singal et. al. [6] respectively. The concepts of fuzzy pre-open sets and fuzzy pre-continuous mappings were introduced by Bin Sahana [2]. In this paper the concepts of fuzzy α-quotient maps, fuzzy semi quotien...

We describe the (co)homology of a certain family of normal subgroups of right-angled Artin groups that contain the commutator subgroup, as modules over the quotient group. We do so in terms of (skew) commutative algebra of squarefree monomial ideals.

COURSE CONTENT: Groups, Examples of groups, Some elementary properties of groups, Subgroups, Cyclic groups, Cosets and Langrange’s theorem, Normal subgroups and Quotient groups, Homomorphisms, The Isomorphism Theorems, Group Actions, orbits and stabilizers, Conjugacy, Class equation of a finite group, Cauchy’s Theorem, The structure of p-groups, The Sylow’s theorems, Some applications of Sylow’...

We study certain groups of isometries of hyperbolic space (including certain hyperbolic Coxeter groups) and normal subgroups with quotient Zν , ν ≥ 1. We show that the associated relative growth series are not rational. This extends results obtained by Grigorchuk and de la Harpe for free groups and Pollicott and the author for surface groups.