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Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ________.
Correct answer is '7'. Can you explain this answer?
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Verified Answer
Let G be a group of 35 elements. Then the largest possible size of a s...
Size of group = Ο(G) = 35
Lagranges theorem says if H is subgroup of G then Ο(H)⏐Ο(G).
So Ο(H) can be 1, 5, 7 or 35.
So largest subgroup size other than G itself is 7.
Lagranges theorem says if H is subgroup of G then Ο(H)⏐Ο(G).
So Ο(H) can be 1, 5, 7 or 35.
So largest subgroup size other than G itself is 7.
Most Upvoted Answer
Let G be a group of 35 elements. Then the largest possible size of a s...
Explanation:
To find the largest possible size of a subgroup of G other than G itself, we need to determine the divisors of the order of G, which is 35 in this case.
Prime Factorization:
First, let's find the prime factorization of 35:
35 = 5 * 7
Divisors:
The divisors of 35 are then obtained by combining the prime factors in different ways:
1, 5, 7, 35
Size of Subgroup:
The size of a subgroup must be a divisor of the order of the group.
Since we are looking for the largest possible size, we need to find the largest divisor of 35 that is less than 35.
From the divisors obtained above, the largest divisor less than 35 is 7.
Therefore, the largest possible size of a subgroup of G other than G itself is 7.
To find the largest possible size of a subgroup of G other than G itself, we need to determine the divisors of the order of G, which is 35 in this case.
Prime Factorization:
First, let's find the prime factorization of 35:
35 = 5 * 7
Divisors:
The divisors of 35 are then obtained by combining the prime factors in different ways:
1, 5, 7, 35
Size of Subgroup:
The size of a subgroup must be a divisor of the order of the group.
Since we are looking for the largest possible size, we need to find the largest divisor of 35 that is less than 35.
From the divisors obtained above, the largest divisor less than 35 is 7.
Therefore, the largest possible size of a subgroup of G other than G itself is 7.
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Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ________.Correct answer is '7'. Can you explain this answer?
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Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ________.Correct answer is '7'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ________.Correct answer is '7'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ________.Correct answer is '7'. Can you explain this answer?.
Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ________.Correct answer is '7'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ________.Correct answer is '7'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ________.Correct answer is '7'. Can you explain this answer?.
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