prove that the subgroup of S4 generated by (1 2) and (1 2)(3 4) is a noncylic group of order 4.
Added by Todd J.
Step 1
We know that G contains the identity element, which we can denote as e = (1)(2)(3)(4). Now, let's consider the elements (1 2) and (1 2)(3 4). Since G is generated by these two elements, it must also contain their product: (1 2) * (1 2)(3 4) = (1 2 3 4). Show more…
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