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If H and K are subgroups of G, then
- a)HK is a subgroup but H ∩ K may not be a subgroup.
- b)H ∩ K is a subgroup but HK may not be a subgroup.
- c)Either (a) or (b).
- d)None of the above.
Correct answer is option 'B'. Can you explain this answer?
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If H and K are subgroups of G, thena)HK is a subgroup but H∩K may ...
In general, the product of two subgroups H and K of a group G, denoted by HK, is not necessarily a subgroup of G. In order for HK to be a subgroup, certain conditions need to be satisfied, such as H and K being normal subgroups or G being an abelian group.
However, we can say that the intersection of H and K, denoted by H ∩ K, is always a subgroup of G. This is because the intersection of any collection of subgroups is itself a subgroup.
To clarify the statement you provided:
a) If H and K are subgroups of G, then HK may or may not be a subgroup of G.
b) If H and K are subgroups of G, then the intersection H ∩ K is always a subgroup of G.
However, we can say that the intersection of H and K, denoted by H ∩ K, is always a subgroup of G. This is because the intersection of any collection of subgroups is itself a subgroup.
To clarify the statement you provided:
a) If H and K are subgroups of G, then HK may or may not be a subgroup of G.
b) If H and K are subgroups of G, then the intersection H ∩ K is always a subgroup of G.
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If H and K are subgroups of G, thena)HK is a subgroup but H∩K may not be a subgroup.b)H ∩ K is a subgroup but HK may not be a subgroup.c)Either (a) or (b).d)None of the above.Correct answer is option 'B'. Can you explain this answer?
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If H and K are subgroups of G, thena)HK is a subgroup but H∩K may not be a subgroup.b)H ∩ K is a subgroup but HK may not be a subgroup.c)Either (a) or (b).d)None of the above.Correct answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If H and K are subgroups of G, thena)HK is a subgroup but H∩K may not be a subgroup.b)H ∩ K is a subgroup but HK may not be a subgroup.c)Either (a) or (b).d)None of the above.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If H and K are subgroups of G, thena)HK is a subgroup but H∩K may not be a subgroup.b)H ∩ K is a subgroup but HK may not be a subgroup.c)Either (a) or (b).d)None of the above.Correct answer is option 'B'. Can you explain this answer?.
If H and K are subgroups of G, thena)HK is a subgroup but H∩K may not be a subgroup.b)H ∩ K is a subgroup but HK may not be a subgroup.c)Either (a) or (b).d)None of the above.Correct answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If H and K are subgroups of G, thena)HK is a subgroup but H∩K may not be a subgroup.b)H ∩ K is a subgroup but HK may not be a subgroup.c)Either (a) or (b).d)None of the above.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If H and K are subgroups of G, thena)HK is a subgroup but H∩K may not be a subgroup.b)H ∩ K is a subgroup but HK may not be a subgroup.c)Either (a) or (b).d)None of the above.Correct answer is option 'B'. Can you explain this answer?.
Solutions for If H and K are subgroups of G, thena)HK is a subgroup but H∩K may not be a subgroup.b)H ∩ K is a subgroup but HK may not be a subgroup.c)Either (a) or (b).d)None of the above.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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