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

Question

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

• A. Commutativity
• B. Associativity
• C. Existence of inverse for every element
• D. Existence of identity

Comments

Same question from GATE CS 2009

link : https://gateoverflow.in/795/gate2009-1

Answer 1

• 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.