Commensurator
In group theory, a branch of abstract algebra, the commensurator of a subgroup H of a group G is a specific subgroup of G.
Definition
The commensurator of a subgroup H of a group G, denoted commG(H) or by some comm(H),[1] is the set of all elements g of G that conjugate H and leave the result commensurable with H. In other words,
Properties
- commG(H) is a subgroup of G.
- commG(H) = G for any compact open subgroup H.
See also
Notes
References
- Geoghegan, Ross (2008), Topological Methods in Group Theory, Graduate Texts in Mathematics, Springer, ISBN 978-0-387-74611-1.
- Onishchik, A.L.; Vinberg, E.B. (2000), Lie groups and Lie algebras II, Encyclopaedia of mathematical sciences, Springer, ISBN 3-540-50585-7.
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