A perfect code in a graph $$\Gamma $$ is subset C of $$V(\Gamma )$$ such that no two vertices are adjacent and every vertex ){\setminus } C$$ to exactly one C. Let G be finite group G. Then said if there exists Cayley admiting as code. It proved subgroup H only Sylow 2-subgroup This result provides way simplify the study codes general groups 2-groups. As an application, criterion for determinin...

This paper finds the Artin characters and exponent dependingon character table conjugacy classes of projective special lineargroup PSL (2,P*).Then we prove that (2, P*) isequal to p*' where P is a prime number , p=3 k> 0.

Mat r x ( F q ) o f a l l r b y r m a t r i c e s o v e r F q , b y C t h e g r o u p G L t i ( F q ) o f t h e u n i t s of M, and by S the special linear subgroup SL , (F q ) o f C . F o r a n a r b i t r a r y field F containing F q , l e t U s t a n d f o r t h e ( c o m m u t a t i v e ) p o l y n o m i a l a l g e b r a F[xl, , x r ] , a n d c o n s i d e r U g r a d e d a s u s u a l : U...

At the 1988 Oberwolfach Computational Group Theory meeting, Joachim Neubiiser asked for an efficient algorithm to decide whether the subgroup of the general linear group GL(d, q) generated by a given set X of non-singular d X d matrices over a finite field ¥q contains the special linear group SL(rf, q). Amplifying the problem he said he would be happy to have a program that could be used for ge...