## If regular representation of a group G contains an odd permutation, then G has a subgroup of index 2

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.2 Exercise 4.2.12 Solution: If $\pi[G] \leq S_G$ contains an odd permutation, then $\pi[G] \not\leq A_G$. Now $A_G \vartriangleleft…