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20D: Abstract Finite Groups


In this section we discuss finite groups only. Moreover, we study the internal properties of those groups -- material on their representation (20C) or permutation actions (20B) or cohomology (20J) are for now on the main group theory page. One may characterize this page as holding all those results about group theory for which a consideration of the order of elements is a central part of the question.

We include here some topics in permutation groups when the groups are obviously finite (e.g. the Rubik group), although these will eventually be moved to a separate section 20B.


Sylow. Frattini. Burnside. Brauer. Then the whole classification of finite simple groups. Après ça, la deluge.

Applications and related fields

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Parent field: 20: Group Theory and Generalizations

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

Well-known textbooks

"Reviews on finite groups", classified by Daniel Gorenstein. American Mathematical Society, Providence, 1974, 706 pp. -- reviews published 1940-1970 in Mathematical Reviews.

Software and tables

Other web sites with this focus

Selected topics at this site

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Last modified 2000/01/14 by Dave Rusin. Mail: