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If G is a group and H a subgroup of G, x is an element in G, and h is an element in H the cosets of H in G are defined as follows:

  • Left coset: xH is the set of all the elements h of H multiplied by x on the left.
  • Right coset: Hx is the set of all the elements h of H multiplied by x on the right.

When xH = Hx we say that H is normal in G.de:Gruppentheorie#Nebenklassenru:Глоссарий теории групп#К

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