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Let G be an Abelian group o f order 10. Let S = {g ε G : g-1 = g}. Then the number of nonidentity elements in S is :
- a)5
- b)2
- c)1
- d)0
Correct answer is option 'C'. Can you explain this answer?
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Let G be an Abelian group o f order 10. Let S = {g ε G : g-1 =...
An idempotent element in a monoid is one that, when combined with itself, produces the same element. Mathematically, this is expressed as a² = a * a = a.
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Let G be an Abelian group o f order 10. Let S = {g ε G : g-1 =...
G is abelian group of order 10.
S= {g ε G ; g-1 = g }
e ε S Since, G contains 10 elements apart from unity, each element will have its inverse. So such pair will form even number of element. There will be atleast one element left that element will be its own inverse.
Thus, S will contain one non unity element.
S= {g ε G ; g-1 = g }
e ε S Since, G contains 10 elements apart from unity, each element will have its inverse. So such pair will form even number of element. There will be atleast one element left that element will be its own inverse.
Thus, S will contain one non unity element.
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Let G be an Abelian group o f order 10. Let S = {g ε G : g-1 =...
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