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The number of non abelian groups of order 12 under isomorphism is a)0 b)1 c)3 d)4?
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The number of non abelian groups of order 12 under isomorphism is a)0 ...
Non-Abelian Groups of Order 12
In this problem, we need to determine the number of non-abelian groups of order 12 under isomorphism.
Non-Abelian Groups
A non-abelian group is a group that is not commutative, i.e., there exist elements a and b such that ab is not equal to ba.
Order of a Group
The order of a group is the number of elements in the group. For a group of order 12, the possible partitions of the number 12 into divisors are 1, 2, 2, 3; 1, 2, 4, 2; 1, 3, 4, 1; 2, 2, 3, 1.
Possible Non-Abelian Groups of Order 12
1. The only non-abelian group of order 12 up to isomorphism is the symmetric group S3. It has 6 elements and is non-abelian.
Therefore, the correct answer is b) 1. There is only 1 non-abelian group of order 12 under isomorphism.
In this problem, we need to determine the number of non-abelian groups of order 12 under isomorphism.
Non-Abelian Groups
A non-abelian group is a group that is not commutative, i.e., there exist elements a and b such that ab is not equal to ba.
Order of a Group
The order of a group is the number of elements in the group. For a group of order 12, the possible partitions of the number 12 into divisors are 1, 2, 2, 3; 1, 2, 4, 2; 1, 3, 4, 1; 2, 2, 3, 1.
Possible Non-Abelian Groups of Order 12
1. The only non-abelian group of order 12 up to isomorphism is the symmetric group S3. It has 6 elements and is non-abelian.
Therefore, the correct answer is b) 1. There is only 1 non-abelian group of order 12 under isomorphism.
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The number of non abelian groups of order 12 under isomorphism is a)0 b)1 c)3 d)4?
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The number of non abelian groups of order 12 under isomorphism is a)0 b)1 c)3 d)4? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The number of non abelian groups of order 12 under isomorphism is a)0 b)1 c)3 d)4? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of non abelian groups of order 12 under isomorphism is a)0 b)1 c)3 d)4?.
The number of non abelian groups of order 12 under isomorphism is a)0 b)1 c)3 d)4? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The number of non abelian groups of order 12 under isomorphism is a)0 b)1 c)3 d)4? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of non abelian groups of order 12 under isomorphism is a)0 b)1 c)3 d)4?.
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