The Uniqueness of Groups of Lyons Type
نویسندگان
چکیده
We give the first computer free proof of the uniqueness of groups of type Ly. We also show that certain simpicial complexes associated to the Lyons group Ly have the same homotopy type as the Quillen complex for Ly at the prime 3; we show this complex is simply connected, and we calculate its homology. Finally we supply simplified proofs of some properties of groups of type Ly, such as the group order. A group of type Ly is a finite group G possessing an involution t such that H = CG(t) is the covering group of the alternating group AJ1 and t is not weakly closed in H with respect to G. We prove
منابع مشابه
On the Fischer-Clifford matrices of a maximal subgroup of the Lyons group Ly
The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated parti...
متن کاملExistence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations
In this paper, we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations. By a priori estimates, difference and variation techniques, we establish the existence and uniqueness of weak solutions of this problem.
متن کاملThe Uniqueness of a Certain Type of Subdirect Product
We introduce the "$type{lffs}$ subdirect product" and show that every ring is uniquely a $type{lffs}$ subdirect product of a family of $simple{basicls}$ rings. Also we show some applications.
متن کاملExistence and uniqueness of the solution of fuzzy-valued integral equations of mixed type
In this paper, existence theorems for the fuzzy Volterra-Fredholm integral equations of mixed type (FVFIEMT) involving fuzzy number valued mappings have been investigated. Then, by using Banach's contraction principle, sufficient conditions for the existence of a unique solution of FVFIEMT are given. Finally, illustrative examples are presented to validate the obtained results.
متن کاملOn existence and uniqueness of solutions of a nonlinear Volterra-Fredholm integral equation
In this paper we investigate the existence and uniqueness for Volterra-Fredholm type integral equations and extension of this type of integral equations. The result is obtained by using the coupled fixed point theorems in the framework of Banach space $ X=C([a,b],mathbb{R})$. Finally, we give an example to illustrate the applications of our results.
متن کامل