منابع مشابه
Infinite-dimensional General Linear Groups Are Groups of Universally Finite Width
Recently George Bergman proved that the symmetric group of an infinite set possesses the following property which we call by the universality of finite width: given any generating set X of the symmetric group of an infinite set Ω, there is a uniform bound k such that any permutation σ ∈ Sym(Ω) is a product of at most k elements of X∪X. Bergman also formulated a sort of general conjecture statin...
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Hence, it is easy to count the orbits of GL n q under the conjugation action of U n q but seems hard to do the same for the group U n q itself! We fix some further notation. Let V n q be the vector space of column vectors, a module for GL n q . Recall that a flag is a totally ordered set of n− 1 nonzero proper subspaces of V n q . For g in GL n q let f g be the number of flags fixed by g, so it...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1954
ISSN: 0002-9947
DOI: 10.2307/1990744