2. Consider the groups (R, +) and (R x R, +). Define the map:RX (RX R) → Rx R defined by r(x, y) = (x+ry, y).(a). Show that this map is a group action.(b). Find Orb ((1, 0)), Orb((1, 1)) and Stab((0, 0)).

Given: The group is, (ℝ, +) and (ℝ×ℝ, +) The map is, ℝ×(ℝ×ℝ)→ℝ×ℝ To find: a) The defined map is an…

Answered: 2. Consider the groups (R, +) and (R x…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 5E

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2. Consider the groups (R, +) and (R x R, +). Define the map : RX (RX R) → Rx R defined by r(x, y) = (x+ry, y). (a). Show that this map is a group action. (b). Find Orb ((1, 0)), Orb((1, 1)) and Stab((0,0)).