Solution. Let np denote the number of p-Sylow subgroups. Since n11 is 1 mod 11 and divides 12, we know n11 is either 1 or 12. If it is 1, then it is normal and we are done. So instead, assume n11 is 12. Then there must be 120 elements of order 11 in G, leaving only 12 more elements available. Since n3 is 1 mod 3 and divides 44, we know that n3 is 1, 4 or 22. If it is 1, then again it is normal ...

Let X be a smooth projective connected curve of genus g ≥ 2 defined over an algebraically closed field k of characteristic p > 0. Let G be a finite group, P a Sylow p-subgroup of G and NG(P ) its normalizer in G. We show that if there exists an étale Galois cover Y → X with group NG(P ), then G is the Galois group wan étale Galois cover Y → X , where the genus of X depends on the order of G, th...

Let x be an element of prime order, p, in a finite group, G, and let P be a p-Sylow subgroup of G containing x. Say that x satisfies the unique conjugacy condition (u.c.c.) relative to G and the p-Sylow subgroup P if x is not conjugate in G to any other element of P. Let 02'(G) denote the largest normal subgroup of G oi odd order. Define the subgroup Z*(G) by the equation Z*(G)/0v(G)=Z(G/0v(G))...

Suppose that G is an abelian p-separable group and R is a commutative unital ring of prime characteristic p. It is proved that if Rp i possesses nilpotent elements for each natural number i, then the normalized Sylow p-subgroup S(RG) in the group ring RG is torsion-complete if and only if G is p-bounded. This supplies our recent results from Acta Math. Hung. (1997), Ric. Mat. (2002), Tamkang J....

Let G be a finite group and let T (G) be the abelian group of equivalence classes of endotrivial kG-modules, where k is an algebraically closed field of characteristic p. We determine, in terms of the structure of G, the kernel of the restriction map from T (G) to T (S), where S is a Sylow p-subgroup of G, in the case when S is abelian. This provides a classification of all torsion endotrivial ...