Description
Groups and symmetries
Tuesday, June 29, 2021
3:29 PM
math103a-s-21 Page 1
Symmetric group
Tuesday, June 29, 2021
3:29 PM
math103a-s-21 Page 2
Symmetric group
Tuesday, June 29, 2021
3:29 PM
math103a-s-21 Page 3
Symmetric group
Tuesday, June 29, 2021
3:29 PM
math103a-s-21 Page 4
Dihedral group
Tuesday, June 29, 2021
3:29 PM
math103a-s-21 Page 5
Dihedral group
Tuesday, June 29, 2021
3:29 PM
math103a-s-21 Page 6
Dihedral group
Tuesday, June 29, 2021
3:29 PM
math103a-s-21 Page 7
Dihedral group
Tuesday, June 29, 2021
3:29 PM
math103a-s-21 Page 8
Dihedral group
Tuesday, June 29, 2021
3:29 PM
math103a-s-21 Page 9
Dihedral group
Tuesday, June 29, 2021
3:29 PM
math103a-s-21 Page 10
An idea for symmetries of a graph
Tuesday, June 29, 2021
3:29 PM
math103a-s-21 Page 11
4. Suppose G is an infinite path whose vertices are integer points and i E Z is connected to exactly two
points i – 1 and i + 1. Let o : Z → Z,0(x):= x +1 and T: Z → Z, 7(2):= -2.
(a) Prove that o and T are symmetries of G.
(b) Prove that if y is a symmetry of G and 7(0) = 0 and y(1) = 1, then y is the identity map.
(c) Prove that if y is a symmetry of G, 7(0) = 0, 7(1) = -1, then y=t.
(d) Prove that Sym(G) = {o’li E Z} U{olotli E Z}.
Purchase answer to see full
attachment