1. ## Subgroups

Hello all. Could you please help me to determine whether or not these are subgroups. Thanks, James

$G:=\Sigma_4$, $S=\left\{(a b)(c d)\right\}$ where the elements a,b,c,d are 1,2,3,4 (in any order, though must be distinct)

$G:=\Sigma_5$, $S=\left\{(a b)(c d)\right\}$ where the elements a,b,c,d are 1,2,3,4,5 (in any order, though must be distinct)

2. Originally Posted by alittletouched
Hello all. Could you please help me to determine whether or not these are subgroups. Thanks, James

$G:=\Sigma_4$, $S=\left\{(a b)(c d)\right\}$ where the elements a,b,c,d are 1,2,3,4 (in any order, though must be distinct)

$G:=\Sigma_5$, $S=\left\{(a b)(c d)\right\}$ where the elements a,b,c,d are 1,2,3,4,5 (in any order, though must be distinct)
Basically all you need to show is if $x,y\in S$ then $xy\in S$.