mjhjmtu

Clash Royale CLAN TAG #URR8PPP 2 $begingroup$ I have $theta,tau, sigmain S_7$ , where $theta=(13)(14)(567), tau=(137)(2456), sigma=(13456)(27)$ . I need to find $sigma langlethetaranglecaptaulanglethetarangle$ . I approached this by first computing $langlethetarangle$ . I got $langlethetarangle=(13)(24)(567),(576),(13)(24),(675),(13)(24)(576),id$ . I then worked out the left coset $sigmalanglethetarangle$ by multiplying $(13456)(27)$ by every element in $langlethetarangle$ , one by one. That gave me $(1574632),(134726),(274563),(1346)(257),(263)(457)$ . Using the same technique, I found $taulanglethetarangle$ to be $(357)(46),(136247),(37)(456),(1357)(246),(3647),id$ . But then I get $sigmalanglethetaranglecaptaulanglethetarangle=phi$ , since there are no elements occurring in both $sigmalanglethetarangle$ and $taulanglethetarangle$ . Why is the intersection empty? If I have done this right, is there an easier way to tell that the intersection of two cosets will be e...

"Australian" redirects here. For other uses, see Australian (disambiguation). Australians Flag of Australia Total population c.  26 million Regions with significant populations   Australia 25,000,000   United States 94,000–200,000 [1] [2]   United Kingdom 113,000 [3]   Hong Kong 90,000 [4] [5]   New Zealand 70,000 [6]   Canada 62,910 [7]   Indonesia 55,000 [8]   Greece 50,000   Italy 30,000 [8] [9]   Lebanon 20,000–25,000 [8] [10]   Singapore 20,000 (2011) [11]   Sweden 7,942 [12]   France 3,000 (2011) [13]   Brazil 1,000 [14] Languages English  · Other minority languages [15] Religion Christianity (Protestantism, Roman Catholicism), Buddhism, Hinduism, Islam and Other minority religions [16] Related ethnic groups British Irish New Zealanders Canadians Americans South Africans British diaspora in Africa White Zimbabweans Melanesians Polynesians Commonwealth Citizens Australians , colloqui...