Keller's conjecture for certain p-groups

P-class Groups of Certain Extensions of Degree P

Let p be an odd prime number. In this article we study the distribution of p-class groups of cyclic number fields of degree p, and of cyclic extensions of degree p of an imaginary quadratic field whose class number is coprime to p. We formulate a heuristic principle predicting the distribution of the p-class groups as Galois modules, which is analogous to the Cohen-Lenstra heuristics concerning...

On Thompson's Conjecture for Alternating Groups A p+3

Let G be a group. Denote by π(G) the set of prime divisors of |G|. Let GK(G) be the graph with vertex set π(G) such that two primes p and q in π(G) are joined by an edge if G has an element of order p · q. We set s(G) to denote the number of connected components of the prime graph GK(G). Denote by N(G) the set of nonidentity orders of conjugacy classes of elements in G. Alavi and Daneshkhah pro...

$L^p$-Conjecture on Hypergroups

In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions  for a weighted Lebesgue space  $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$.  Among the other things, we also show that if $K$ is a locally compact hyper...

Newton Polygons and P-divisible Groups: a Conjecture by Grothendieck

THE SEGAL CONJECTURE FOR ELEMENTARY ABELIAN p-GROUPS-II. p-ADIC COMPLETION IN EQUIVARIANT COHOMOLOGY

This result implies an analogue for general finite groups, but we refer the reader to [25] and especially [S] for that. We shall give as efficient a proof of the theorem as present technology seems to allow, starting from the purely algebraic Ext calculation [4,1.1] of Adams, Gunawardena, and Miller as a given. When G=(Zp)‘, the theorem is due to those authors. However, their original passage f...