Stable group theory and approximate subgroups
نویسندگان
چکیده
منابع مشابه
Stable Group Theory and Approximate Subgroups
We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sum-product phenomenon. For a simple linear group G, we show that a finite subset X with |XXX|/|X| bounded is close to a finite subgroup, or else to a subset of a proper algebraic subgroup of G. We also find a connection with Lie groups, and use it to obtain some consequences s...
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Next we had talks on Hrushovski’s paper above. The notes below on sections 2 and 3 are a record of talks by Henson and myself, assume only rudimentary knowledge of model theory, and give detailed proofs. If possible we choose notations and formulations similar to those in Hrushovski’s paper. More to follow. Needless to say, the source for all this is [3] to which we also refer for references to...
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1. Introduction. In this paper, we study the fixed point sets and stable subgroups of automorphisms of a connected algebraic linear group over an algebraically closed field of arbitrary characteristic. [7] contains a description of most of the results of this paper, and some material in [7] is essential for the present paper. Many of the results discussed in the present paper were proved at cha...
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We started our research with the intent on answering the following question: can we find a way to calculate all the subgroups of the symmetric group. This is easier said that done, as the number of subgroups for a symmetric group grows quickly with each successive symmetric group. This problem can actually be simplified to finding the subgroup conjugacy classes. So now we have the slightly diff...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2012
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-2011-00708-x