4.The groupofsymmetries of the square is called Dg, and consists ofelements Po: P1: P2, P3, H1, H2, 81, 82. It has the following multiplication table:Po P1 P2 | Pp3 | µ1 | µ2 | 81 | ô2PoPoP1P2P3H2 81 82P1P1P2P3PoP2P2P3PoP1P3P3PoP1P2d2 2 01PoP2P3P1PoP1P3P1P3PoP2P3P1P2Po(a) Show that H = {po,P1, P2; P3} is an abelian subgroup of D1.(b) Find the indices [D: H] and [D : (12)] of H and (u2) in D4.

Answered: Image /qna-images/answer/0d615538-953e-41fb-939c-7b21c177bc92.jpg

4. The group of symmetries of the square is called Dg, and consists of elements Po: P1 P2: P3: H1, H2, 81, 82. It has the following multiplication table: Po | Pi | P2 | P3 | 41 | 42 | ô1 | 82 Po Po P1 P2 P3 H2 81 82 P1 P1 P2 P3 Po P2 P2 P3 Po P1 P3 P3 Po P1 P2 d2 2 01 Po P2 P3 P1 Po P1 P3 P1 P3 Po P2 d2 | H2 | 81 P3 P1 P2 Po (a) Show that H = {po,P1, P2; P3} is an abelian subgroup of D1. (b) Find the indices [D: H] and [D1: (µ2)] of H and (u2) in D..

4. The group of symmetries of the square is called Dg, and consists of elements Po: P1 P2: P3: H1, H2, 81, 82. It has the following multiplication table: Po | Pi | P2 | P3 | 41 | 42 | ô1 | 82 Po Po P1 P2 P3 H2 81 82 P1 P1 P2 P3 Po P2 P2 P3 Po P1 P3 P3 Po P1 P2 d2 2 01 Po P2 P3 P1 Po P1 P3 P1 P3 Po P2 d2 | H2 | 81 P3 P1 P2 Po (a) Show that H = {po,P1, P2; P3} is an abelian subgroup of D1. (b) Find the indices [D: H] and [D1: (µ2)] of H and (u2) in D..

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.1: The Geometry And Algebra Of Vectors

Problem 30EQ: Write out the addition and multiplication tables for 5.

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