let $mathfrak{f}$ be a formation and $g$ a finite group. a subgroup $h$ of $g$ is said to be weakly $mathfrak{f}_{s}$-quasinormal in $g$ if $g$ has an $s$-quasinormal subgroup $t$ such that $ht$ is $s$-quasinormal in $g$ and $(hcap t)h_{g}/h_{g}leq z_{mathfrak{f}}(g/h_{g})$, where $z_{mathfrak{f}}(g/h_{g})$ denotes the $mathfrak{f}$-hypercenter of $g/h_{g}$. in this paper, we study the structur...

In this paper we prove that if G is a finite group of automorphisms of a ring R, where the order of G is a unit in R, then R is fully integral of degree m(|G|) over the fixed ring R. Here m is a function of the order of G. This gives a positive answer to a well-known question of S. Montgomery and extends the result of D. S. Passman for abelian group actions. Our theorem can be viewed as a gener...

We consider the question of which loops are capable of expressing arbitrary Boolean functions through expressions of constants and variables. We call this property Boolean completeness. It is a generalization of functional completeness, and is intimately connected to the computational complexity of various questions about expressions, circuits, and equations defined over the loop. We say that a...

Classically, the nilpotence theorem of Devinatz, Hopkins, and Smith tells us that non-nilpotent self maps on finite p-local spectra induce nonzero homomorphisms on BP -homology. Motivically, over C, this theorem fails to hold: we have a motivic analog of BP and whilst η : S1,1 → S0,0 induces zero on BP -homology, it is nonnilpotent. Recent work with Haynes Miller has led to a calculation of ηπ∗...

We consider the following problem: Given a term t, a rewrite system R, a finite set of equations E′ such that R is E′-convergent, compute finitely many instances of t: t1, . . . , tn such that, for every substitution σ, there is an index i and a substitution θ such that tσ↓ =E′ tiθ (where tσ↓ is the normal form of tσ w.r.t. →E′\R). The goal of this paper is to give equivalent (resp. sufficient)...

In the 1980’s, Ravenel introduced sequences of spectra X(n) and T(n) which played an important role in proof Nilpotence Theorem Devinatz–Hopkins–Smith. present paper, we solve homotopy limit problem for topological Hochschild homology X(n), is a generalized version Segal Conjecture cyclic groups prime order. This result first step towards computing algebraic K-theory using trace methods, approx...

This paper addresses the problem of computing the family of two-filiform Lie algebra laws of dimension nine using three Lie algebra properties converted into matrix form properties: Jacobi identity, nilpotence and quasi-filiform property. The interest in this family is broad, both within the academic community and the industrial engineering community, since nilpotent Lie algebras are applied in...

We investigate the inteplay between the algebraic structure of a group G and arithmetic properties of its spectrum σ(G) which consists of the eigenvalues of all the inner automorphisms of G. A complex number λ is called an eigenvalue of a group automorphism A : G → G if φ ◦ A|H = λ · φ for some non-trivial homomorphism φ : H → C defined on an A-invariant subgroup H ⊂ G. It is shown that many pr...

Fix a field F. A zero-nonzero pattern A is said to be potentially nilpotent over F if there exists a matrix with entries in F with zero-nonzero pattern A that allows nilpotence. In this paper an investigation is initiated into which zero-nonzero patterns are potentially nilpotent over F with a special emphasis on the case that F = Zp is a finite field. A necessary condition on F is observed for...