Isomorphism of p-adic group rings

Isomorphisms of p-adic group rings

A long-standing problem, first posed by Graham Higman [15] and later by Brauer [4] is the “isomorphism problem for integral group rings.” Given finite groups G and H, is it true that ZG = ZH implies G 2: H? Many authors have worked on this question, but progress has been difficult [30]. Perhaps the best positive result was that of Whitcomb in 1968 [37], who showed that the implication G = H hol...

Group Rings over the p-Adic Integers

ENUMERATION OF ISOMORPHISM CLASSES OF EXTENSIONS OF p-ADIC FIELDS

Let Ω be an algebraic closure of Qp and let F be a finite extension of Qp contained in Ω. Given positive integers f and e, the number of extensions K/F contained in Ω with residue degree f and ramification index e was computed by Krasner. This paper is concerned with the number I(F, f, e) of F -isomorphism classes of such extensions. We determine I(F, f, e) completely when p2 ∤ e and get partia...

A NOTE ON p-ADIC INVARIANT INTEGRAL IN THE RINGS OF p-ADIC INTEGERS

In [2], I constructed the p-adic q-integral I q (f) on Z p. In this paper, we consider the properties of lim q→−1 I q (f) = I −1 (f). Finally we give the some applications of I −1 (f) and integral equations for I −1 (f). These properties are useful and worthwhile to study Euler numbers and polynomials.

ISOMORPHISM OF COMMUTATIVE GROUP ALGEBRAS OF p-MIXED SPLITTING GROUPS OVER RINGS OF CHARACTERISTIC ZERO

Suppose G is a p-mixed splitting abelian group and R is a commutative unitary ring of zero characteristic such that the prime number p satisfies p / ∈ inv(R)∪ zd(R). Then R(H) and R(G) are canonically isomorphic R-group algebras for any group H precisely when H and G are isomorphic groups. This statement strengthens results due to W.May published in J.Algebra (1976) and to W.Ullery published in...