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..
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![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 P1 P2 | Pp3 | µ1 | µ2 | 81 | ô2
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
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 [D : (12)] of H and (u2) in D4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a4dcd82-baf4-45bc-b40b-693a3e683492%2F0d615538-953e-41fb-939c-7b21c177bc92%2Fy7hn1c9_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 P1 P2 | Pp3 | µ1 | µ2 | 81 | ô2
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
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 [D : (12)] of H and (u2) in D4.
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