A Class of Finite Simple Bol Loops of Exponent 2

نویسنده

  • GÁBOR P. NAGY
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 (2005). These results answer some questions of M. Aschbacher.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Se p 20 07 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 [3]. These results answer some questions of M. Aschbacher.

متن کامل

A 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 کامل

A 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 کامل

On 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

A Class of Bol Loops with a Subgroup of Index Two

Let G be a finite group and C2 the cyclic group of order 2. Consider the 8 multiplicative operations (x, y) 7→ (xiyj)k, where i, j, k ∈ {−1, 1}. Define a new multiplication on G × C2 by assigning one of the above 8 multiplications to each quarter (G× {i})× (G× {j}), for i, j ∈ C2. We describe all situations in which the resulting quasigroup is a Bol loop. This paper also corrects an error in P....

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008