UP TGT Mathematics Set Theory Test Series - Part 1
If |G| = 35, what are the possible orders of elements in G?
Type: MCQ • Marks: 1
If |G| = 35, what are the possible orders of elements in G?
Options
A. 1, 5, 7, 35
B. 1 and 35 only
C. 5 and 7 only
D. 1, 2, 5, 7, 35
Explanation
Correct Answer: Option 1 (1, 5, 7, 35). Lagrange's Theorem states that for any finite group G, the order of every subgroup H divides the order of G (|G| = |H| * [G : H]). Hence element orders also divide |G|.
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