1. Prove that the subgroup of A4 generated by any element of order 2 and and any element of order 3 is all of A4.
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I need to use the following two Lemmas which are simple facts for group theory.
Lemma1: Suppose is a group and is a subgroup of . If , then is a normal subgroup of .
Lemma2: has unique normal subgroup .
(a) Suppose are arbitrary ...
This solution uses the following two Lemmas which are simple facts for group theory.