Multiple choice

Which one of the following in 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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A Correct answer
Explanation

A group requires four properties: closure (implicit), associativity, identity element, and inverses. Commutativity (ab = ba for all a,b) is NOT required - groups with commutativity are called 'abelian groups'. So commutativity is the correct answer as the non-required property.

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