how to raise permutation groups to a power  TOPIC_SOLVED

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.

how to raise permutation groups to a power

Postby 113256 on Wed May 07, 2014 7:20 pm

how do you raise a permutation group to a power. i know how to do it for small powers like 2 but how do you find T^387

T =
(1 2 3 4 5 6 7 8)
(3 4 5 2 7 8 1 6)
113256
 
Posts: 1
Joined: Wed May 07, 2014 7:18 pm

Sponsor

Sponsor
 

Re: how to raise permutation groups to a power  TOPIC_SOLVED

Postby nona.m.nona on Thu May 08, 2014 12:03 am

113256 wrote:how do you raise a permutation group to a power. i know how to do it for small powers like 2 but how do you find T^387

T =
(1 2 3 4 5 6 7 8)
(3 4 5 2 7 8 1 6)

This permutation may be written in cyclic form as T = (1 3 5 7)(2 4)(6 8). The order of this permutation is the least common multiple (LCM) of the lengths of these cycles; the lengths are 4, 2, and 2, so the order of T is 4. Because the permutations within T are disjoint, multiplication is associative and commutative. Thus, T^4 = (1 3 5 7)(2 4)(6 8)*(1 3 5 7)(2 4)(6 8)*(1 3 5 7)(2 4)(6 8)*(1 3 5 7)(2 4)(6 8) = (1 3 5 7)^4 * (2 4)^4 * (6 8)^4 = (1 3 5 7)(2 4)(6 8) = T.

Using this information, how might you reduce the power on T^387 to be a more manageable value?
nona.m.nona
 
Posts: 249
Joined: Sun Dec 14, 2008 11:07 pm


Return to Discrete Math