Symmetric Generation of Groups
نویسندگان
چکیده
Some of the most beautiful mathematical objects found in the last forty years are the sporadic simple groups, but gaining familiarity with these groups presents problems for two reasons. Firstly, they were discovered in many different ways, so to understand their constructions in depth one needs to study lots of different techniques. Secondly, since each of them is, in a sense, recording some exceptional symmetry in space of certain dimensions, they are by their nature highly complicated objects with a rich underlying combinatorial structure.
منابع مشابه
Gait Generation for a Bipedal System By Morris-Lecar Central Pattern Generator
The ability to move in complex environments is one of the most important features of humans and animals. In this work, we exploit a bio-inspired method to generate different gaits in a bipedal locomotion system. We use the 4-cell CPG model developed by Pinto [21]. This model has been established on symmetric coupling between the cells which are responsible for generating oscillatory signals. Th...
متن کاملA NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS
The commuting graph of a group is a graph with vertexes set of a subset of a group and two element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the symmetric groups. The clique number, coloring number, independent number, and diameter of these graphs are also computed.
متن کاملFuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks
Fuchsian groups (acting as isometries of the hyperbolic plane) occur naturally in geometry, combinatorial group theory, and other contexts. We use character-theoretic and probabilistic methods to study the spaces of homomorphisms from Fuchsian groups to symmetric groups. We obtain a wide variety of applications, ranging from counting branched coverings of Riemann surfaces, to subgroup growth an...
متن کاملFlag-transitive Point-primitive symmetric designs and three dimensional projective special linear groups
The main aim of this article is to study (v,k,λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3,q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2,q) and G > PSL(3,q).
متن کاملCubic symmetric graphs of orders $36p$ and $36p^{2}$
A graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. In this paper, we classifyall the connected cubic symmetric graphs of order $36p$ and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.
متن کاملBinary Linear Codes and Symmetric Generation of Finite Simple Groups
In this paper, we study a new combinatorial method to construct decodable binary linear codes for which the automorphism groups are generated by sets of involutory symmetric generators. In this method codewords as elements of a group are represented as permutations in Sn followed by words in the n involutory symmetric generators. Transformation between elements written in symmetric representati...
متن کامل