Question 11596 – Arrays
January 28, 2024Question 17412 – ISRO CS-2023
January 28, 2024Question 10270 – GATE 1994
Some group (G,o) is known to be abelian. Then, which one of the following is true for G?
Correct Answer: C
Question 10 Explanation:
Associate property of a group (aob)oc = ao(boc)
For Abelian group, commutative also holds
i.e., (aob) = (boa)
Consider option (C):
(goh)2 = (goh)o(gog)
= (hog)o(goh)
= (ho(gog)oh)
= ((hog2)oh)
= (g2oh)oh
= g2o(hoh)
= g2oh2 [True]
For Abelian group, commutative also holds
i.e., (aob) = (boa)
Consider option (C):
(goh)2 = (goh)o(gog)
= (hog)o(goh)
= (ho(gog)oh)
= ((hog2)oh)
= (g2oh)oh
= g2o(hoh)
= g2oh2 [True]
g = g-1 for every g ∈ G
g = g2 for every g ∈ G
(goh)2 = g2oh2 for every g,h ∈ G
G is of finite order
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