Determine which of the following sets G, with the indicated operation is a group. Which is anabelian group?Note: clearly show that the conditions for G under the operation of o to be a group are satisfiedand if G has an identity element, state what that element is, if elements of G have an inverse,state what the inverse of an element would look like.(a) Given the sets R* and Z, let G = R* ×Z. Define a binary operation o on G by (a,m)o(b, n) =(ab, m+n).(b) Let G = R XR with the origin deleted. Define a binary operation o on G by (a, b) o (c,d) =(ac - bd, ad + bc).(c) Would the result in part (b) change if the origin was included in G?

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.2: Properties Of Group Elements

Problem 27E: 27. Suppose that is a nonempty set that is closed under an associative binary operation and that...

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