Show that the set of matrices \(\{a, b, c, d\}\) given by

closes under multiplication and is a representation of the group \(\mathrm{D}_{2}\) in Problem 2.9 .

Data from Problem  2.9

Show that the group {e, a, b, c\} with multiplication table (b) below, is in one to one correspondence with the geometrical symmetry operations on figure (a) below

This is called the 4-group or dihedral group \(\mathrm{D}_{2}\). Show that \(\mathrm{D}_{2}\) has three subgroups, \(\{e, a\},\{e, b\}\), and \(\{e, c\}\), each isomorphic to the cyclic group \(\mathrm{C}_{2}\).

Transcribed Image Text:

1 a b = (9) = ( 9 ) = ( d ) d = (o C = ( 0 9 )