UP TGT Mathematics Set Theory Test Series - Part 1
If H is a subgroup of G and a in G, the set aH = {ah : h in H} is called:
Type: MCQ • Marks: 1
If H is a subgroup of G and a in G, the set aH = {ah : h in H} is called:
Options
A. Center of H
B. Right coset of H in G
C. Normalizer of H
D. Left coset of H in G
Explanation
Correct Answer: Option 4 (Left coset of H in G). Cosets aH partition the group G into mutually disjoint equivalence classes of equal size |H|. The number of distinct left cosets is the index [G : H].
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