1. If (G,*) a group such that a² = e for all a € G. Prove that G is abelian. 2. Define an operation on G=R x R\{0} as follows: (a, b) (c,d) = (a + bc, bd) for all (a, b), (c,d) € G. Show that (G, *) is a group. Is G abelian?
1. If (G,*) a group such that a² = e for all a € G. Prove that G is abelian. 2. Define an operation on G=R x R\{0} as follows: (a, b) (c,d) = (a + bc, bd) for all (a, b), (c,d) € G. Show that (G, *) is a group. Is G abelian?
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 12E: Prove or disprove that H={ hGh1=h } is a subgroup of the group G if G is abelian.
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Transcribed Image Text:1. If (G,*) a group such that a² = e for all a € G. Prove that G is
abelian.
2. Define an operation on G =R x R\{0} as follows:
(a, b) (c,d) = (a + bc, bd) for all (a, b), (c,d) € G.
Show that (G, *) is a group. Is G abelian?
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