2. Let R = R – {1} be the set of all real numbers except one. Define a binary operationon R by a * b = a + b + ab, Va, b, E R. Prove (R, *) is a group. Is it abelian? Is (Q, *) asubgroup? Is (Ž, *) a subgroup?

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Answered: 2. Let R = R – {1} be the set of all…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 31E: Exercises 31. Let be a group with its center: . Prove that if is the only element of order in ,...

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2. Let R = R – {1} be the set of all real numbers except one. Define a binary operation on R by a * b = a + b + ab,Va, b, E R. Prove (R, *) is a group. Is it abelian? Is (Q, *) a subgroup? Is (2, *) a subgroup?

2. Let R = R – {1} be the set of all real numbers except one. Define a binary operation on R by a * b = a + b + ab,Va, b, E R. Prove (R, ) is a group. Is it abelian? Is (Q, ) a subgroup? Is (2, *) a subgroup?