منابع مشابه
A Theorem on Lie Groups
Roughly, the theorem says that each subgroup near enough to G* can be transformed into G* by an appropriate element of G. This result can be regarded as a generalization of the known fact that Lie groups cannot have arbitrarily small subgroups (other than the identity), although it was not from this point of view that our interest arose. To make our meaning clear, assume that G* is an invariant...
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If A is a finite subset of a free group with at least two noncommuting elements then |A · A · A| ≥ |A| 2 (log |A|)O(1) . More generally, the same conclusion holds in an arbitrary virtually free group, unless A generates a virtually cyclic subgroup. The central part of the proof of this result is carried on by estimating the number of collisions in multiple products A1 · . . . · Ak. We include a...
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Glauberman’s classical Z∗-theorem is a theorem about involutions of finite groups (i.e. elements of order 2). It is one of the important ingredients for the classification of finite simple groups, which in turn allows to prove the corresponding theorem for elements of arbitrary prime order p. Let us recall the statement: if G is a finite group with a Sylow p-subgroup P , and if x is an element ...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2015
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-015-0326-7