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In the symmetric group Sn of degree n,n > 2 the set of all 3-cycles generates a subgroup of order
- a)3
- b)3n
- c)n!/2
- d)n!
Correct answer is option 'C'. Can you explain this answer?
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In the symmetric group Sn of degree n,n > 2 the set of all 3-cycles...
Hence the correct option is n!/2
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In the symmetric group Sn of degree n,n > 2 the set of all 3-cycles...
The symmetric group Sn of degree n is the group of all permutations of n elements. In other words, it is the group of all possible ways to rearrange the elements {1, 2, ..., n}.
The order of the symmetric group Sn is n!, which is the number of possible permutations of n elements.
The symmetric group Sn is a non-abelian group, meaning that the order in which permutations are composed matters. For example, if we consider the permutations (1 2) and (2 3) in S3, where (1 2) swaps 1 and 2, and (2 3) swaps 2 and 3, then their composition is (1 2)(2 3) = (1 3), which swaps 1 and 3. This shows that the composition of permutations is not commutative.
The symmetric group Sn is a finite group, as it consists of a finite number of permutations. However, it is an infinite group in the limit as n approaches infinity, as there are an infinite number of ways to permute an infinite set.
The symmetric group Sn has many interesting properties and applications in various areas of mathematics, including combinatorics, group theory, and algebraic geometry. It is widely studied and has connections to many other important mathematical structures and concepts.
The order of the symmetric group Sn is n!, which is the number of possible permutations of n elements.
The symmetric group Sn is a non-abelian group, meaning that the order in which permutations are composed matters. For example, if we consider the permutations (1 2) and (2 3) in S3, where (1 2) swaps 1 and 2, and (2 3) swaps 2 and 3, then their composition is (1 2)(2 3) = (1 3), which swaps 1 and 3. This shows that the composition of permutations is not commutative.
The symmetric group Sn is a finite group, as it consists of a finite number of permutations. However, it is an infinite group in the limit as n approaches infinity, as there are an infinite number of ways to permute an infinite set.
The symmetric group Sn has many interesting properties and applications in various areas of mathematics, including combinatorics, group theory, and algebraic geometry. It is widely studied and has connections to many other important mathematical structures and concepts.
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In the symmetric group Sn of degree n,n > 2 the set of all 3-cycles...
Even permutations generate alternating group
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In the symmetric group Sn of degree n,n > 2 the set of all 3-cycles generates a subgroup of ordera)3b)3nc)n!/2d)n!Correct answer is option 'C'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about In the symmetric group Sn of degree n,n > 2 the set of all 3-cycles generates a subgroup of ordera)3b)3nc)n!/2d)n!Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the symmetric group Sn of degree n,n > 2 the set of all 3-cycles generates a subgroup of ordera)3b)3nc)n!/2d)n!Correct answer is option 'C'. Can you explain this answer?.
In the symmetric group Sn of degree n,n > 2 the set of all 3-cycles generates a subgroup of ordera)3b)3nc)n!/2d)n!Correct answer is option 'C'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about In the symmetric group Sn of degree n,n > 2 the set of all 3-cycles generates a subgroup of ordera)3b)3nc)n!/2d)n!Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the symmetric group Sn of degree n,n > 2 the set of all 3-cycles generates a subgroup of ordera)3b)3nc)n!/2d)n!Correct answer is option 'C'. Can you explain this answer?.
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