Exercise · ZW-GROUP-008 · ★★☆ Intermediate
The identity of a group must...
Choose one option.
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- C. Leave every element fixed when operating
Explanation
The identity e leaves every element fixed when operating: e ∗ a = a ∗ e = a for all a. It does not change from one element to another (it is unique) and it need not be the only element of the group.
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-001 Which list contains the axioms of a 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-009 Which of these conditions is NOT a group axiom?