1-closed subset

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Definition

Symbol-free definition

A nonempty subset of a group is termed a 1-closed subset if it satisfies the following equivalent conditions:

  1. It is a union of subgroups
  2. It is a power-closed symmetric subset
  3. For any element in it, the cyclic subgroup generated by that element is also in it. In particular, it is a union of cyclic subgroups.

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