منابع مشابه
Representing Quotients of Permutation Groups
IN this note, we consider the following problem. Let G be a finite permutation group of degree d, and let N b e a normal subgroup of G. Under what circumstances does G/N have a faithful permutation representation of degree at most di Positive answers to this question are likely to have applications to computational group theory, since there are currently no really satisfactory practical methods...
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By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...
متن کاملQuotients of Algebraic Groups
In this note, we study the existence and structure of the homogeneous space G/H for algebraic groups H ⊂ G. Let k be a field. All schemes considered will be k-schemes. By an affine algebraic group, we mean an affine group scheme of finite type over k. Note that we do not assume our schemes are reduced yet. We will only consider affine algebraic groups. From now on, G will denote an algebraic gr...
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The maximality of Abelian subgroups play a role in various parts of group theory. For example, Mycielski [8, 7] has extended a classical result of Lie groups and shown that a maximal Abelian subgroup of a compact connected group is connected and, furthermore, all the maximal Abelian subgroups are conjugate. For finite symmetric groups the question of the size of maximal Abelian subgroups has be...
متن کاملQuotients of CI-Groups are CI-Groups
We show that a quotient group of a CI-group with respect to (di)graphs is a CI-group with respect to (di)graphs. In [1,2], Babai and Frankl provided strong constraints on which finite groups could be CI-groups with respect to graphs. As a tool in this program, they proved [1, Lemma 3.5] that a quotient group G/N of a CI-group G with respect to graphs is a CI-group with respect to graphs provide...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1998
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700031907