When N is a normal subgroup of G, can we reconstruct G from N and G/N? In general, no. For instance, the groups Z/(p2) and Z/(p) × Z/(p) (for prime p) are nonisomorphic, but each has a cyclic subgroup of order p and the quotient by it also has order p. As another example, the nonisomorphic groups Z/(2p) and Dp (for odd prime p) have a normal subgroup that is cyclic of order p, whose quotient is...

We introduce a way of describing cohomology of the symmetric groups Σn with coefficients in Specht modules. We study H (Σn, S λ R) for i ∈ {0, 1, 2} and R = Z, Fp. The focus lies on the isomorphism type of H(Σn, S λ Z ). Unfortunately, only in few cases can we determine this exactly. In many cases we obtain only some information about the prime divisors of |H(Σn, S λ Z )|. The most important to...

A new recursive procedure to compute the Zassenhaus formula up to high order is presented, providing each exponent in the factorization directly as a linear combination of independent commutators and thus containing theminimumnumber of terms. The recursion can be easily implemented in a symbolic algebra package and requires much less computational effort, both in time and memory resources, than...

We describe a new simplified version of the Cantor-Zassenhaus polynomial factorization algorithm, which entails a lower computational cost. The key point is to use linear test polynomials, which not only reduce the computational burden, but also enable us to derive good estimates and deterministic bounds on the number of attempts needed to factor a given polynomial. Mathematics Subject Classifi...

We present an algorithm for factoring polynomials over local fields, in which the Montes algorithm is combined with elements from Zassenhaus Round Four algorithm. This algorithm avoids the computation of characteristic polynomials and the resulting precision problems that occur in the Round Four algorithm.