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Sticky Note
If every element of a group G is its own inverse then G is called?
  1. Cyclic
  2. Abelian
  3. Finite
  4. None of these
Explanation
  • If every element of a group GG is its own inverse, then g2=eg^2 = e for all g∈Gg in G, meaning all elements are of order 2.
  • Such a group is Abelian because the group operation commutes: (gh)2=e(gh)^2 = e implies gg and hh must commute.

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