A closed subalgebra of a Banach algebra is called maximal if it is not contained in any larger proper closed subalgebra. Let G be a discrete abelian topological group and L its group-algebra, i.e. L is the Banach algebra of functions/on G with E*e<J |/(X)| < °° and multiplication defined as convolution. What are the maximal subalgebras of L? The complete answer is not known even when G is the g...

Let G be a linear algebraic group defined over Q, and assume that G(R) is compact and meets every connected component of G(C). Let Q̂ := Ẑ ⊗ Q be the ring of finite adèles. Every arithmetic subgroup Γ of G(Q) is finite, and is obtained by choosing an open, compact subgroup K of G(Q̂) and defining Γ = K ∩G(Q) in G(Q̂). We note that G(Q) is discrete and co-compact in G(Q̂). In this paper, we consider...

the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...

In papers by Semmes [6], Macpherson and Neumann [4] and Brazil, Covington, Penttila, Praeger and Woods [2], it has been shown that stabilizers of filters (equivalently, stabilizers of ideals) play a crucial role in the study of maximal subgroups of infinite symmetric groups. Semmes proved that if if is a maximal subgroup of S = Sym (Q), where Q is a set of infinite cardinality K and H contains ...

Abstract We study toric G -solid Fano threefolds that have at most terminal singularities, where is an algebraic subgroup of the normalizer a maximal torus in their automorphism groups. All varieties are assumed to be projective and defined over field complex numbers.

Let G be a finite group, and let F be a formation of finite group. We say that a subgroup H of G is p F -normal in G if there exists a normal subgroup T of G such that HT is a permutable Hall subgroup of G and G G H H T H / ) ( is contained in the F-hypercenter ) / ( G F H G Z of G H G / . In this note, we get some results about the p F -normal subgroups and then use them to study the structure...

Abstract Let p be a prime. A pro- group G is said to 1-smooth if it can endowed with continuous representation $\theta \colon G\to \mathrm {GL}_1(\mathbb {Z}_p)$ such that every open subgroup H of , together the restriction \vert _H$ satisfies formal version Hilbert 90. We prove contains unique maximal closed abelian normal subgroup, in analogy result by Engler and Koenigsmann on Galois groups ...

THIS paper concerns maximal subgroups of symmetric groups on infinite, usually countable, sets. Our main aim is to give examples of maximal subgroups which could claim to be almost stabilisers of familiar combinatorial structures. We emphasise that maximal subgroup always means maximal proper subgroup. Throughout this paper, Cl will denote an infinite set, usually countable. The power set of Q ...

1.1. Aschbacher-Scott Program. Primitive permutation groups have been studied since Galois and Jordan and have applications in many different areas. If Γ is a transitive permutation group with a point stabilizer M then Γ is primitive if and only if M < Γ is a maximal subgroup. So studying primitive permutation groups is equivalent to studying maximal subgroups. In most problems involving a fini...

With every nontrivial connected algebraic group G we associate a positive integer gtd(G) called the generic transitivity degree of G and equal to the maximal n such that there is a nontrivial action of G on an irreducible algebraic variety X for which the diagonal action of G on Xn admits an open orbit. We show that gtd(G) 6 2 (respectively, gtd(G) = 1) for all solvable (respectively, nilpotent...