Let G be a finite group, p prime, and (K,O,F) p-modular system. We prove that the trivial source ring of OG is isomorphic to coherent G-stable tuples (χP), where χP virtual character K[NG(P)/P], P runs through all p-subgroups G, coherence condition equality certain values. use this result describe group orthogonal units as product unit Burnside fusion system with (φP) homomorphisms NG(P)/P→F×. ...

MR0004042 (2,309c) 20.0X Brauer, R.; Nesbitt, C. On the modular characters of groups. Annals of Mathematics. Second Series 42 (1941), 556–590. The authors first summarize the theory of modular characters of a finite group G as previously developed by them [Univ. of Toronto Studies, Math. Series, no. 4, 1937]. If an element of G is defined to be p-regular when its order is prime to p, one of the...

We introduce a strong form of Oliver’s p-group conjecture and derive a reformulation in terms of the modular representation theory of a quotient group. The Sylow p-subgroups of the symmetric group Sn and of the general linear group GLn(Fq) satisfy both the strong conjecture and its reformulation.

a $p$-group $g$ is $p$-central if $g^{p}le z(g)$‎, ‎and $g$ is‎ ‎$p^{2}$-abelian if $(xy)^{p^{2}}=x^{p^{2}}y^{p^{2}}$ for all $x,yin‎ ‎g$‎. ‎we prove that for $g$ a finite $p^{2}$-abelian $p$-central ‎$p$-group‎, ‎excluding certain cases‎, ‎the order of $g$ divides the ‎order of $text{aut}(g)$‎.

Let V be a representation of the modular group Γ of dimension p. We show that the Z-graded space H(V ) of holomorphic vector-valued modular forms associated to V is a free module of rank p over the algebra M of classical holomorphic modular forms. We study the nature of H considered as a functor from Γ-modules to graded M-lattices and give some applications, including the calculation of the Hil...

We relate a part of the abelian étale fundamental group of curves over local fields to the component group of the Néron model of the jacobian. We apply the result to the modular curve X0(p)/Qp to show that the unramified abelian covering X1(p) → X0(p) (Shimura covering) uses up all the possible ramification over the special fiber of X0(p).

BACKGROUND The Rejuvenate modular-neck stem implant (Stryker Orthopaedics, Mahwah, New Jersey) was recently recalled due to corrosion at the femoral neck-stem junction. The purpose of this study was to investigate the rate of corrosion-related failure and survivorship of this implant and analyze the correlation of implant and patient factors with serum metal ion levels and revisions. METHODS ...

This is a study of weakly integral braided fusion categories with elementary rules to determine which possess nondegenerately extensions theoretically minimal dimension, or equivalently in this case, satisfy the modular extension conjecture. We classify near-group satisfying conjecture; remaining Tambara-Yamagami provide arbitrarily large families identical violating These examples generalize r...

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.