Commensurator

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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[edit]

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,

[2]

Properties[edit]

  • commG(H) is a subgroup of G.
  • commG(H) = G for any compact open subgroup H.

See also[edit]

Notes[edit]

  1. ^ Onishchick (2000), p. 94
  2. ^ Geoghegan (2008), p. 348

References[edit]