Order set-determined group

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This group property is about the given group being determined, upto isomorphism, by certain statistic(s)

Definition

A finite group G is said to be order set-determined if given any other group H such that:

  • G and H have the same order (i.e. total cardinality)
  • The set of orders of elements of G is the same as the set of orders of elements of H

then H must be isomorphic to G.

Relation with other properties

Stronger properties