Characterization of Frobenius Groups of Special Type

We define a Con-Cos group G to be one having a proper normal subgroup N whose cosets other than N itself are conjugacy classes. It follows easily that N = G’, the derived group of G. Most of the paper is devoted to trying to classify finite Con-Cos groups satisfying the additional requirement that N has just two conjugacy classes. We show that for such groups the center Z(G) has order at most 2, and if Z(G) = {1}, then G is a Frobenius group of a rather special type.</p

A Framework for Comparing Groups of Documents

We present a general framework for comparing multiple groups of documents. A bipartite graph model is proposed where document groups are represented as one node set and the comparison criteria are represented as the other node set. Using this model, we present basic algorithms to extract insights into similarities and differences among the document groups. Finally, we demonstrate the versatility of our framework through an analysis of NSF funding programs for basic research.Comment: 6 pages; 2015 Conference on Empirical Methods in Natural Language Processing (EMNLP '15

Smarandache mukti-squares

We have introduced Smarandache quasigroups which are Smarandache non-associative structures. A quasigroup is a groupoid whose composition table is a Latin square. There are squares in the Latin squares which seem to be of importance to study the structure of Latin Squares. We consider the particular type of squares properly contained in the Latin squares which themselves contain a Latin square. Such Latin squares are termed as Smarandache Mukti-Squares or SMS. Extension of some SMS to Latin squares is also considered

Smarandache Half-Groups

In this paper we introduce the concept of half-groups. This is a totally new concept and demands considerable attention

Achievable rate region for three user discrete broadcast channel based on coset codes

We present an achievable rate region for the general three user discrete memoryless broadcast channel, based on nested coset codes. We characterize 3-to-1 discrete broadcast channels, a class of broadcast channels for which the best known coding technique\footnote{We henceforth refer to this as Marton's coding for three user discrete broadcast channel.}, which is obtained by a natural generalization of that proposed by Marton for the general two user discrete broadcast channel, is strictly sub-optimal. In particular, we identify a novel 3-to-1 discrete broadcast channel for which Marton's coding is \textit{analytically} proved to be strictly suboptimal. We present achievable rate regions for the general 3-to-1 discrete broadcast channels, based on nested coset codes, that strictly enlarge Marton's rate region for the aforementioned channel. We generalize this to present achievable rate region for the general three user discrete broadcast channel. Combining together Marton's coding and that proposed herein, we propose the best known coding technique, for a general three user discrete broadcast channel.Comment: A non-additive 3-user discrete broadcast channel is identified for which achievable rate region based on coset codes is analytically proven to be strictly larger than that achievable using unstructured iid codes. This version is submitted to IEEE Transactions on Information Theor

Computing sum of sources over an arbitrary multiple access channel

The problem of computing sum of sources over a multiple access channel (MAC) is considered. Building on the technique of linear computation coding (LCC) proposed by Nazer and Gastpar [2007], we employ the ensemble of nested coset codes to derive a new set of sufficient conditions for computing the sum of sources over an \textit{arbitrary} MAC. The optimality of nested coset codes [Padakandla, Pradhan 2011] enables this technique outperform LCC even for linear MAC with a structural match. Examples of nonadditive MAC for which the technique proposed herein outperforms separation and systematic based computation are also presented. Finally, this technique is enhanced by incorporating separation based strategy, leading to a new set of sufficient conditions for computing the sum over a MAC.Comment: Contains proof of the main theorem and a few minor corrections. Contents of this article have been accepted for presentation at ISIT201