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Permutation groups. (English) Zbl 0845.20001
Graham, R. L. (ed.) et al., Handbook of combinatorics. Vol. 1-2. Amsterdam: Elsevier (North-Holland). 611-645 (1995).
This is a survey of the current state of permutation group theory (mostly finite).
The paper begins with a discussion of the reduction to primitive permutation groups, a straightforward presentation (without proof) of the O’Nan-Scott theorem, and a description of the finite simple groups. Applications are given, for example to the classification theorems of finite doubly transitive and rank three permutation groups, to upper bounds on the order of a primitive permutation group (in terms of the degree) and to distance transitive graphs. A brief account is given of applications of character theory to finite permutation groups, followed by an introduction to characters of the symmetric groups. There are also some remarks on computing algorithms in permutation group theory, and on infinite permutation groups.
For the entire collection see [Zbl 0833.05001].

MSC:
20B05 General theory for finite permutation groups
20-02 Research exposition (monographs, survey articles) pertaining to group theory
20B40 Computational methods (permutation groups) (MSC2010)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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