Yes, I understand that 51 is not a prime, but 51 is a multiple of 3 and 17.
So, I'm using this theorem:
Theorem 1. Suppose G is a non-Abelian group whose order is divisible by at least two
distinct primes and all of whose proper subgroups have prime-power order. Then
(i) absolutevalue[G]...
Homework Statement
a) Classify all groups of order 51.
b) Classify all groups of order 39.
Homework Equations
Sylow theorems.
The Attempt at a Solution
a) C51
b) Z3 X Z13
and Z13 x Z3, the semi-direct product with presentation <a,b|a13=b3=1, ab=a3 >
Are these all of the...
Homework Statement
Solve the inhomogeneous differential equation dX/dt=AX+B in terms of the solutions to the homogeneous equation dX/dt=AX.
Homework Equations
A is an nxn real or complex matrix and X(t) is an n-dimensional vector-valued function.
If v is an eigenvector for A with...