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NIELIT 2016 DEC Scientist B (CS) - Section B: 28

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Which one of the following is NOT necessarily a property of a Group?

  1. Commutativity
  2. Associativity
  3. Existence of inverse for every element
  4. Existence of identity
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  • Groupoid: closure property.
  • Semigroup: closure, associative.
  • Monoid-closure: associative, identity.
  • Group: closure, associative, identity, inverse.
  • Abelian group: group properties + commutativity 

So, ans should be A.

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