We demonstrate that two supersoluble complements of an abelian base in a finite split extension are conjugate if and only if, for each prime $p$, Sylow $p$-subgroup one complement is to the other. As corollary, we find any subgroup $N$ $G$ there exists $S$ such $S\cap N$ $G$. In particular, restricting groups allows us ease D. G. Higman's stipulation be within $S$. then consider group actions o...

In this paper, we find a strong new restriction on the structure of CI-groups. We show that, if R is generalised dihedral group and CI-group, then for every odd prime p Sylow p-subgroup has order p, or 9. Consequently, any CI-group with quotient same restriction, that

Consider the Jacobian of a genus two curve defined over a finite field and with complex multiplication. In this paper we show that if the l-Sylow subgroup of the Jacobian is not cyclic, then the embedding degree of the Jacobian with respect to l is one.

In this paper, we construct a group with three real irreducible characters whose Sylow 2-subgroup is an iterated central extension of a Suzuki 2-group. This answers a question raised by Moretó and Navarro who asked whether such a group exists. MSC primary: 20C15

We construct arcs K of cardinality 2q + 1 in the projective space PG(3, q3), q = ph, p > 3 prime, from a cubic curve C. By construction, K is stabilized by a p-Sylow subgroup of the projectivities preserving C and it is contained in no twisted cubic of PG(3, q3). Mathematics Subject Classification: 51A30, 51E20, 51E21

We classify the permutation groups of cyclic codes over a finite field. As a special case, we find the permutation groups of non-primitive BCH codes of prime length. In addition, the Sylow p-subgroup of the permutation group is given for many cyclic codes of length p. Several examples are given to illustrate the results.

We present a recursive construction for difference sets which unifies the Hadamard, McFarland, and Spence parameter families and deals with all abelian groups known to contain such difference sets. The construction yields a new family of difference sets with parameters (v, k, *, n)=(2(2&1) 3, 2(2+1) 3, 2(2+1) 3, 2) for d 0. The construction establishes that a McFarland difference set exists in ...

Perfect isometries and isotypies are constructed for alternating groups between blocks with abelian defect groups and the Brauer correspondents of these blocks. These perfect isometries and isotypies satisfy additional compatibility conditions which imply that an extended Broué conjecture holds for the principal block of an almost simple group with an abelian Sylow psubgroup and a generalized F...

Let P be an extraspecial p-group which is neither dihedral of order 8, nor of odd order p and exponent p. Let G be a finite group having P as a Sylow p-subgroup. Then the mod-p cohomology ring of G coincides with that of the normalizer NG(P ).

We describe an algorithm due to Gauss, Shanks and Lagarias that, given a non-square integer D 0; 1 mod 4 and the factorization of D, computes the structure of the 2-Sylow subgroup of the class group of the quadratic order of discriminant D in random polynomial time in log jDj.