UP TGT Mathematics Set Theory Test Series - Part 1
If H is a subgroup of K and K is a subgroup of G (for finite groups), then [G : H] is:
Type: MCQ • Marks: 1
If H is a subgroup of K and K is a subgroup of G (for finite groups), then [G : H] is:
Options
A. [K : H] / [G : K]
B. [G : K] + [K : H]
C. [G : K] * [K : H]
D. [G : K] / [K : H]
Explanation
Correct Answer: Option 3 ([G : K] * [K : H]). 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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