Abstract Let p be a an odd prime and let G finite -group with cyclic commutator subgroup $G^{\prime }$ G ′ . We prove that the exponent abelianization of centralizer in are determined by group algebra over any field characteristic If, additionally...

Galois group, 222adeles, 149Artin’s conjecture, 293automorphic form, 292bar resolution, 172biquadratic reciprocity, 271Brauer group, 205Brauer-Hasse-Noether theorem, 252central simple algebra, 206centralizer, 206chain map, 163change of group, 184Chebotarev density theorem, 282class formation, 222class group, 33cohomological functor, 16...

Let X be a non-degenerate left Banach module over a normed algebra A having a bounded approximate left identity. We show that, if A is a left ideal of a larger algebra, then this representation can be extended to a representation of the larger algebra. Based on this result, we study in detail the existence and properties of representations of the various centralizer algebras of A which are comp...

Let W be an arbitrary Coxeter group, possibly of infinite rank. We describe a decomposition of the centralizer ZW (WI) of an arbitrary parabolic subgroup WI into the center of WI , a Coxeter group and a subgroup defined by a 2-cell complex. Only information about finite parabolic subgroups is required in an explicit computation. Moreover, by using our description of ZW (WI), we reveal a further...

The diagram algebra introduced by Brauer that describes the centralizer algebra of the n-fold tensor product of the natural representation of an orthogonal Lie group has a presentation by generators and relations that only depends on the path graph An−1 on n− 1 nodes. Here we describe an algebra depending on an arbitrary graph M , called the Brauer algebra of type M , and study its structure in...

Here we consider all finite non-abelian 2-generator $p$-groups ($p$ an odd prime) of nilpotency class two and study the probability of having $n^{th}$-roots of them. Also we find integers $n$ for which, these groups are $n$-central.

Given a field F , a scalar λ ∈ F and a matrix A ∈ F, the twisted centralizer code CF (A, λ) := {B ∈ F | AB − λBA = 0} is a linear code of length n. When A is cyclic and λ 6= 0 we prove that dimCF (A, λ) = deg(gcd(cA(t), λcA(λt))) where cA(t) denotes the characteristic polynomial of A. We also show how CF (A, λ) decomposes, and we estimate the probability that CF (A, λ) is nonzero when |F | is f...

INTRODUCTION Femoral centralizers in total hip arthroplasty (THA) are designed to improve the neutral implant position and ensure a homogeneous cement mantle without implant-bone impingement. To date there are no data about the cement mantle configuration and implant position after malinsertion, as seen in mini-open approaches or adipose patients with a limited view. The present biomechanical s...