Mathematics · Group Theory
Let S 5 be the symmetric group on five symbols. Which of the following statements is false?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1S 5 does not contain a subgroup of order 7
- 2S 5 does not contain a subgroup isomorphic to &DoubleStruckCapitalZ;/2&DoubleStruckCapitalZ; × &DoubleStruckCapitalZ;/2&DoubleStruckCapitalZ;✓
- 3S 5 contains a non-Abelian subgroup of order 8
- 4S 5 contains a cyclic subgroup of order 6
Correct answer
S 5 does not contain a subgroup isomorphic to &DoubleStruckCapitalZ;/2&DoubleStruckCapitalZ; × &DoubleStruckCapitalZ;/2&DoubleStruckCapitalZ;
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