منابع مشابه
Images of Word Maps in Finite Simple Groups
In response to questions by Kassabov, Nikolov and Shalev, we show that a given subset A of a finite simple group G is the image of some word map w : G×G → G if and only if (i) A contains the identity and (ii) A is invariant under Aut(G).
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In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced. Of course, the solution will have a considerable effect on many related areas, both wi...
متن کاملWord Values in Finite Groups
Let w = w(x1, ..., xd) denote a group word in d variables, that is, an element of the free group of rank d. For a finite group G we may define a word map that sends a d-tuple, (g1, ..., gd) of elements of G, to its w-value, w(g1, ..., gd), by substituting variables and evaluating the word in G by performing all relevant group operations. In this thesis we study a number of problems to do with t...
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this is a survey article on centralizers of finite subgroups in locally finite, simple groups or lfs-groups as we will call them. we mention some of the open problems about centralizers of subgroups in lfs-groups and applications of the known information about the centralizers of subgroups to the structure of the locally finite group. we also prove the following: let $g$ be...
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The Algebraicity Conjecture treats model-theoretic foundations of algebraic group theory. It states that any simple group of finite Morley rank is an algebraic group over an algebraically closed field. In the mid-1990s a view was consolidated that this project falls into four cases of different flavour: even type, mixed type, odd type, and degenerate type. This book contains a proof of the conj...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2019
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-019-01364-z