Se p 20 07 A CLASS OF FINITE SIMPLE BOL LOOPS OF EXPONENT 2
نویسنده
چکیده
In this paper we give an infinite class of finite simple right Bol loops of exponent 2. The right multiplication group of these loops is an extension of an elementary Abelian 2-group by S5. The construction uses the description of the structure of such loops given by M. Aschbacher [3]. These results answer some questions of M. Aschbacher.
منابع مشابه
A Class of Finite Simple Bol Loops of Exponent 2
In this paper we give an infinite class of finite simple right Bol loops of exponent 2. The right multiplication group of these loops is an extension of an elementary Abelian 2-group by S5. The construction uses the description of the structure of such loops given by M. Aschbacher (2005). These results answer some questions of M. Aschbacher.
متن کاملA ug 2 00 9 Commuting graphs of odd prime order elements in simple groups ∗
We study the commuting graph on elements of odd prime order in finite simple groups. The results are used in a forthcoming paper describing the structure of Bruck loops and Bol loops of exponent 2.
متن کاملA class of simple proper Bol loops ∗ Gábor
For a loop Q, we call the maps La(x) = ax,Ra(x) = xa left and right translations, respectively. These are permutations of Q, generating the left and right multiplication groups LMlt(Q),RMlt(Q) of Q, respectively. The group closure Mlt(Q) of LMlt(Q) and RMlt(Q) is the full multiplication group of Q. Just like for groups, normal subloops are kernels of homomorphisms of loops. The loop Q is simple...
متن کاملCOMPUTATIONAL RESULTS ON FINITE P-GROUPS OF EXPONENT P2
The Fibonacci lengths of the finite p-groups have been studied by R. Dikici and co-authors since 1992. All of the considered groups are of exponent p, and the lengths depend on the celebrated Wall number k(p). The study of p-groups of nilpotency class 3 and exponent p has been done in 2004 by R. Dikici as well. In this paper we study all of the p-groups of nilpotency class 3 and exponent p2. Th...
متن کاملOn a conjecture of a bound for the exponent of the Schur multiplier of a finite $p$-group
Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $exp(G)$ and let $m=lfloorlog_pk floor$. We show that $exp(M^{(c)}(G))$ divides $exp(G)p^{m(k-1)}$, for all $cgeq1$, where $M^{(c)}(G)$ denotes the c-nilpotent multiplier of $G$. This implies that $exp( M(G))$ divides $exp(G)$, for all finite $p$-groups of class at most $p-1$. Moreover, we show that our result is an improvement...
متن کامل