|Algebraic structure||Unital magma|
The wreath product is an product that operates on groups.
Definition[edit | edit source]
Given a group and a permutation group such that , then is a group where:
Put simply the operation permutes the tuple g in the first argument by the permutation h' in the second argument, and then combines the two tuples pairwise with the usual operations.
This definition can be generalized to apply to arbitrary groups, by observing that due to Cayley's theorem every group is isomorphic to a permutation group.
Properties[edit | edit source]
- For groups G and : .
- If and then is isomorphic to a subgroup of Smn.
References[edit | edit source]
- McMahan, Peter (2003). Wreath-Product Polytopes (PDF) (Thesis). Reed College.
- Here n is determined by .