Linear Groups in an Infinite Field
نویسندگان
چکیده
منابع مشابه
A relation between infinite subsets and exterior center in groups
Let G be a group. Neumann to answer a question of Paul Erdos proved that every infinite subset of G has two different comuting elements if and only if G is center-by-finite. In this paper, we deal with Erdoschr('39')s question in different aspect and we show that every infinite subset X of G has two different elements x and y such that x^y=1 if and only if the exterior center of G ihas finit...
متن کاملTopics in Infinite Groups
Preface These are lecture notes for a course taught in Cambridge during Lent 2014 by Jack Button, on a topics in infinite group theory. There are likely to be errors, which are solely the fault of the scribe. If you discover any, please contact me [email protected].
متن کاملInfinite Groups
Most interesting groups arise as a group of transformations. For example the set of “rigid motions” of 2-dimensional space R forms a group denoted Isom(R). There are three kinds of transformations: reflection about a line, rotation about a point, and translation in a direction. These form a group under composition (i.e., do one transformation and then do the other). For example, the composition...
متن کاملInfinite-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...
متن کاملMeasuring sets in infinite groups
We are now witnessing a rapid growth of a new part of group theory which has become known as “statistical group theory”. A typical result in this area would say something like “a random element (or a tuple of elements) of a group G has a property P with probability p”. The validity of a statement like that does, of course, heavily depend on how one defines probability on groups, or, equivalentl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 1901
ISSN: 0024-6115
DOI: 10.1112/plms/s1-34.1.185