Question

2. Find the subgroup (fo, T]) of Sa, where σ (2134 What is the subgroup isomorphic to? 23 order (σ ): 2 L (12) (34) Su

Just trying to figure out what the subgroup is isomorphic to?

Answer 1

Solution :

Given that

To determine  what the subgroup is isomorphic to ?

Let, < {sigma, tau} > sigma = (1 2 2 1 3 3 4 4) tau = (1 1 2 2 3 4 4 3) doublerightarrow sigma = (1 2 2 1 3 3 4 4) tau = (1 1 2 2 3 4 4 3) = (1 2) = (3 4) order (sigma) = 2 and order (tau) = 2 < {sigma, tau} > = < {(1, 2), (3, 4)} > = < sigma, (1, 2), (3, 4), (1, 2), (3, 4) > therefore which is the sub group of s_4 \r\n rightarrow every element of the sets are of order 2 and they are commutes. Therefore Subgroup is isomorphism to klein fourgroup.