Exercise · ZW-GROUP-001 · ★☆☆ Basic
Which list contains the axioms of a group?
Choose one option.
Show answer
- B. Closure, associativity, identity and inverses
Explanation
A group is a set with an operation that is closed, associative, has an identity element and every element has an inverse. Commutativity is not an axiom (only abelian groups have it).
Review the concept: Group
A group is a nonempty set \(G\) together with an associative binary operation, with an identity element and an inverse for every element.
\[(G,\ast)\]
More practice problems: group
- ZW-GROUP-002 Which structure is a group?
- ZW-GROUP-003 Why is (ℤ, ·) not a group?
- ZW-GROUP-004 What is the identity of (ℤ, +)?
- ZW-GROUP-005 What is the inverse of 3 in (ℤ, +)?
- ZW-GROUP-006 Which structure is a group with the indicated operation?
- ZW-GROUP-007 ℕ=\0,1,2,…\ with the usual addition is not a group because...
- ZW-GROUP-008 The identity of a group must...
- ZW-GROUP-009 Which of these conditions is NOT a group axiom?