What are the elements in the subgroup generated by $\langle(1234)\rangle$ in $S_4$?
2026-03-26 09:40:15.1774518015
What are the elements in the subgroup generated by $\langle(1234)\rangle$ in $S_4$?
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Consider the element $(1234)$. It has order $4$, hence $<(1234)>$ has 4 elements : the identity, $(1234)$, $(1234)^2=(13)(24)$, $(1234)^3=(1432)$.