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 Subgroup action on the triple set T(1,2,3,4) are considered.

Triple Caley Table

@	xyx	xyz	zyx	zyz
xyx	1	2	1	2
xyz	1	2	1	2
zyx	3	4	3	4
zyz	3	4	3	4

 

 

LEFT Coset action of Subgroup(a)

1233@	1	2	3	4
1233	1133	2244	1133	2244
(2133)	1133	2244	1133	2244

 

RIGHT Coset of Subgroup (a)

@1233	1233	(2133)
1	1211	2111
2	1211	2111
3	3433	4333
4	3433	4333

 The left and right coset are different. There are no orbits under (a)

LEFT Coset action Subgroup (d)

@	1	2	3	4
2234	1133	2244	1133	2244
2243	1133	2244	1133	2244

 

LEFT Coset action Subgroup (b)

@	1	2	3	4
1244	1133	2244	1133	2244
2144	1133	2244	1133	2244

 

Klein4 Coset Group Action

@	1	2	3	4
1234	1133	2244	1133	2244
2134	1133	2244	1133	2244
1243	1133	2244	1133	2244
2143	1133	2244	1133	2244

 

Klein4 RIGHT Coset

@	1234	2134	1243	2143
1	1212	2112	1221	2121
2	1212	2112	1221	2121
3	3434	4334	3443	4343
4	3434	4334	3443	4343

 

No Orbits. 

 

 

 

 

©Copyright 2007 Dr David McGrath. All rights reserved