theorem 1.31 The set of all rotations about the origin and reflections inlines through the origin is a group called orthogonal group and is denotedby 0(2). SO(2) is a subgroup of index 2 in O(2).Det'n: Let P be any point in E². The set P of all lines that passesthrough P is called pencil of lines through P. We denote REF(P) :REF(P) the smallest group of isometries containing all 24, where l e P.We denote ROT(P) the set of all rotations about P.

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Answered: theorem 1.31 The set of all rotations…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 23E

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