Zassenhaus algebras
نویسندگان
چکیده
منابع مشابه
The Schur–zassenhaus Theorem
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...
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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...
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A metabelian group G of order 1440 is constructed which provides a counterexample to a conjecture of Zassenhaus on automorphisms of integral group rings. The group is constructed in the spirit of [8]. An augmented automorphism of ZG which has no Zassenhaus factorization is given explicitly (this was already done in [7] for a group of order 6720), but this time only a few distinguished group rin...
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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...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2011
ISSN: 0035-7596
DOI: 10.1216/rmj-2011-41-6-1793