منابع مشابه
Maximal Compact Normal Subgroups and Pro-lie Groups
We are concerned with conditions under which a locally compact group G has a maximal compact normal subgroup K and whether or not G/K is a Lie group. If G has small compact normal subgroups K such that G/K is a Lie group, then G is pro-Lie. If in G there is a collection of closed normal subgroups {Ha} such that f~| Ha = e and G/Ha is a Lie group for each a, then G is a residual Lie group. We de...
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for absolute constants C6, C7. This theorem (almost) follows from [EV, Theorem 1.1], the only point being to control the dependence of implicit constants on the degree of the number field. We refer to [EV] for further information and for some motivational comments about the method. In the proof C1, C2, . . . will denote certain absolute constants. A.2. Let K be an extension of Q of degree d ≥ 2...
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What ingredients are necessary to describe all maximal subgroups of the general finite group G? This paper is concerned with providing such an analysis. A good first reduction is to take into account the first isomorphism theorem, which tells us that the maximal subgroups containing a given normal subgroup N of G correspond, under the natural projection, to the maximal subgroups of the quotient...
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A group G is simple if and only if the diagonal subgroup of G ×G is a maximal subgroup. This striking property is very easy to prove and raises the question of determining all the maximal subgroups of G , where G denotes the direct product of n copies of G . The first purpose of this note is to answer completely this question. We show in particular that if G is perfect, then any maximal subgrou...
متن کاملMaximal Subgroups of Symmetric Groups
A theorem of O’Nan and Scott [6]; [2, Chapter 4] restricts the possibilities for maximal subgroups of finite symmetric groups: they are of six types of which the first four are explicitly known, the fifth involves a finite simple group, and the sixth an action of a simple group. This result, in conjunction with the Classification of Finite Simple Groups, has a number of consequences. In particu...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1987
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1987-0870807-9