Exercise · ZW-ORDER-OF-A-GROUP-006 · ★☆☆ Basic
The rotations that leave a square in the same position form a group. What is its order?
Choose one option.
Show answer
- D. 4
Explanation
They are the rotations by \(0^\circ\), \(90^\circ\), \(180^\circ\) and \(270^\circ\): four elements. Adding the reflections the full group would have order 8.
Review the concept: Order of a group
The order of a finite group \(G\) is its number of elements; if \(G\) is infinite it has infinite order.
\[|G|\]
More practice problems: order of a group
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- ZW-ORDER-OF-A-GROUP-003 What is the order of the group (ℤ,+)?
- ZW-ORDER-OF-A-GROUP-004 The group of units mod 12, \x : gcd(x,12)=1\ under multiplication mod 12, has order
- ZW-ORDER-OF-A-GROUP-005 What is the order of the group of units mod 15?
- ZW-ORDER-OF-A-GROUP-007 What is the smallest order a group can have?
- ZW-ORDER-OF-A-GROUP-008 How many elements does the group GL_2(ℤ_2) of invertible 2×2 matrices with entries in ℤ_2 have?
- ZW-ORDER-OF-A-GROUP-009 What is the order of the group of units mod 100?