linear algebraWatch

#1
Hi,
I was wondering if there is any general method of working out the number of elements in a group. For example Consider the ?eld Fp with p elements. Determine the number of elements in the following groups:
(i) GLn(Fp)
(ii) SLn(Fp).
OR
Let F3 be the ?eld with three elements. Let n ? 1. Determine the number of elements in the following groups:
(i) B = {B = (bij ) ? GLn(F3), bij = 0 for i > j}
(ii) U = {B ? B : det(B) = 1}.
0
7 years ago
#2
(Original post by blondie16)
Hi,
I was wondering if there is any general method of working out the number of elements in a group. For example Consider the ?eld Fp with p elements. Determine the number of elements in the following groups:
(i) GLn(Fp)
(ii) SLn(Fp).
OR
Let F3 be the ?eld with three elements. Let n ? 1. Determine the number of elements in the following groups:
(i) B = {B = (bij ) ? GLn(F3), bij = 0 for i > j}
(ii) U = {B ? B : det(B) = 1}.
Say whaaa?
Can you translate all those ambiguous question marks pls?
0
#3
Woops, sorry copied them off some exam papers and didn't notice it hadn't worked properly. The question should be:
I was wondering if there is any general method of working out the number of elements in a group. For example Consider the field Fp with p elements. Determine the number of elements in the following groups:
(i) GLn(Fp)
(ii) SLn(Fp).
OR
Let F3 be the field with three elements. Let n be greater than or equal to 1. Determine the number of elements in the following groups:
(i) B = {B = (bij ) is an element of GLn(F3), bij = 0 for i > j}
(ii) U = {B is an element of B : det(B) = 1}.
0
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