1. Assume (X, o) and (Y,on X x Y asare groups. Let X × Y = {(x, y) |x € X, y € Y} and define the operation *(x1, Y1) * (x2, Y2) = (x1 0 x2, Y1 • Y2)for (x1, y1), (x2,Y2) E X × Y. Show that (X x Y, *) is a group.

The given question is related to group theory. Given: X , ∘ and Y , ∙ are groups. Let X × Y = x,y |…

Answered: Assume (X,o) and (Y, on X x Y as are…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 5E: 5. For any subgroup of the group , let denote the product as defined in Definition 4.10. Prove that...

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Elements Of Modern Algebra

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Assume (X,o) and (Y, on X x Y as are groups. Let X × Y = {(x, y) | æ € X, y E Y} and define the operation * (x1,Y1) * (x2, Y2) = (x1 © x2, Y1 • Y2) for (a1, Y1), (x2, Y2) E X × Y. Show that (X x Y, *) is a group.