40 Permutation Groups

A permutation group is a group of permutations on a finite set W of positive integers. GAP does not require the user to specify the operation domain W when a permutation group is defined.

gap> g:=Group((1,2,3,4),(1,2));
Group( [ (1,2,3,4), (1,2) ] )

Permutation groups are groups and therefore all operations for groups (see Chapter Groups) can be applied to them. In many cases special methods are installed for permutation groups that make computations more effective.

Sections

1. The Natural Action
2. Computing a Permutation Representation
3. Symmetric and Alternating Groups
4. Primitive Groups
5. Stabilizer Chains
6. Randomized Methods for Permutation Groups
7. Construction of Stabilizer Chains
8. Stabilizer Chain Records
9. Operations for Stabilizer Chains
10. Low Level Routines to Modify and Create Stabilizer Chains
11. Backtrack

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