math_stresser
New member
- Joined
- Nov 21, 2007
- Messages
- 4
Use the technique of Cayley's Theorem to explicitly construct an isomorphism map from the additive group Z-sub-6 to a subgroup in S-sub-6.
Cayley's Theorem: Every group G of order n is isomorphic to a subgroup in the symmetric group S-sub-n.
The additive group Z-sub-6 consists of {0,1,2,3,4,5} (each one of those has a "bar" over it; this is also known as Z mod 6) [Sorry- I don't know how else to write it.]
Z-sub-6 is an additive group, but I don't know how to map its elements to a subgroup in S-sub-6.
Will somebody at least help me get started, PLEASE?!?!?
Cayley's Theorem: Every group G of order n is isomorphic to a subgroup in the symmetric group S-sub-n.
The additive group Z-sub-6 consists of {0,1,2,3,4,5} (each one of those has a "bar" over it; this is also known as Z mod 6) [Sorry- I don't know how else to write it.]
Z-sub-6 is an additive group, but I don't know how to map its elements to a subgroup in S-sub-6.
Will somebody at least help me get started, PLEASE?!?!?