Diagonal subgroup

In the mathematical discipline of group theory, for a given group G, the diagonal subgroup of the n-fold direct product Gn is the subgroup

This subgroup is isomorphic to G.

Properties and applications
  • If G acts on a set X, the n-fold diagonal subgroup has a natural action on the Cartesian product Xn induced by the action of G on X, defined by
  • If G acts n-transitively on X, then the n-fold diagonal subgroup acts transitively on Xn. More generally, for an integer k, if G acts kn-transitively on X, G acts k-transitively on Xn.
  • Burnside's lemma can be proven using the action of the twofold diagonal subgroup.
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See also

References
  • Sahai, Vivek; Bist, Vikas (2003), Algebra, Alpha Science Int'l Ltd., p. 56, ISBN 9781842651575.


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