Question

Is the 2-cycle (1 2) in the subgroup H=$< \sigma ,\tau >$ 9 generated by $\sigma$ and $\tau$? Explain answer.

$\sigma =(1 2 3)(4 5)(6 7 8 9)$
$\tau=(1 3)(5 7 8)(4 9)$

Answer 1

=(123)(45) (6789) e = (13) (578) (49) or=:(123) (45) (6789] (13) (578) (49) =(12) (475968) order af 6 7) = eam af order of (12), order (775968)} t = 1 cm {2, 6) = .6 - (07) 2 = 60 70 z) = (12) (475968) (12) (475968) =(456) (7.98) - (02)3 = (az) (o ty? - (12) (475968) (456) (798) = (12) (49)(76)(58) — ☺ locht= (-22 (2) 2. = (456)(799) (456) (798) = (465)(789) — ☺ (67) 5 = (oc) coet = (12) (475968) (465) (739) (12) (486957) ③ (02) 6 = I (since order or iss) Toit>= $1,C12) (475968), (456) (798) (121491276)(58), (465)(789),(12)(486957) cycle (12) & crits INO