Question

Asked Sep 22, 2019

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Find all normal subgroups of *G* where

(a) *G* = *S*_{3},

(b) *G* = *D*_{4}, the group of symmetries of the square,

(c) *G* = *Q*_{4}, the quaternion group

Step 1

To find all the normal subgroups of the given (three) groups

Step 2

(a) the only normal subgroups are the triivial, the alternating and the whole group

Step 3

There are five normal subgroups of G. The obvious ones are the identity, the subgroup generated by the rotation R , (as it is a subgroup of order 2 in G), and t...

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