B***y
发帖数: 83 | 1
You will have to claculate all the elements in the designated subgroup
generated by the preselected elements.
The problem: consider a permutation group, or a finite ordered group G,
choose some elements a_1, a_2, ... ,a_n, try to give a condition or algorithm
to determine whether an element a is in the subgroup generated by a_1,a_2,..
a_n?
Some casual thinking: Let's say we try to determine whether a is in the subgp
generated by a single element, a_1, you have no choice but to calculate all
ele |
|
B***y
发帖数: 83 | 2
some other ideas: maybe you can compare two subgps given by
{a, a_1, a_2, ...., a_n} and {a_1,a_2,..a_n} and try to show that they are
different or not if you have a specific a... |
|
y**t
发帖数: 50 | 3 D4 has 2 Z2 X Z2, 1 Z4, 5 Z2, 1 D4, and 1 trivial
2 Z2 X Z2 correspond to Q(\sqrt(2)) and Q(I \sqrt(2))
1 Z4 corresponds to Q(I)
1 D4 corresponds to Q,1 trivial corresponds to K
5 Z2 correponds to Q(\sqrt(2), I),Q(a), Q(b), Q(a+b), Q(a-b)
where I^2=-1, a^2=\sqrt(2)+1(e.g. take the plus sqrt as a)
b^2=1-\sqrt(2)
check for yourself before take it as final answer,good luck |
|
