We show that regular homogeneous two-weight Z pk -codes where p is odd and k > 2 with dual Hamming distance at least four do not exist. The proof relies on existence conditions for the strongly regular graph built on the cosets of the dual code.

The general structure of the scalar cosets of the Maxwell-Einstein supergravities is given. Following an introduction of the non-linear coset formalism of the supergravity theories a comparison of the coset algebras of the Maxwell-Einstein supergravities in various dimensions is discussed.

We present coset conformal field theories whose spectrum is not determined by the identification current method. In these “maverick” cosets there is a larger symmetry identifying primary fields than under the identification current. We find an A-D-E classification of these mavericks.

We give an algorithm for enumerating cosets of a group defined as a finite homomorphic image of a semi-direct product of free products of cyclic groups by a group of monomial automorphisms. Lots of finite groups, including some of the sporadic simple groups can be defined in this mannar. Mathematics Subject Classification: 20Bxx

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 ...

1. Reminder on quotient groups Let G be a group and H a subgroup of G. We have seen that the left cosets xH of H in G give a partition of G. Motivated by the case of quotients of rings by ideals, it is natural to consider the product operation on cosets. Recall that for any subsets S, T of G, by ST we mean {st | s ∈ S, t ∈ T }. If G is commutative, the product of two left cosets is another left...

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’...

Let Γ be a torsion-free hyperbolic group. We show that the set of solutions of any system of equations with one variable in Γ is a finite union of points and cosets of centralizers if and only if any two-generator subgroup of Γ is free.

Let F denote the finite field with two elements. We describe a construction of partitions of F , for n = 2 − 1, m ≥ 4, into cosets of pairwise distinct Hamming codes (we call such codes nonparallel) of length n. We give a lower bound for the number of different such partitions.