Find equilibrium solutions for the following ODE initial-value
problem and linearize the problem about those solutions
z" = z − z^3,
z(0) = z0
z'(0) = v0
i found the equilibrium solutions to be 0,1,-1. what are the steps to linearize the problem around these?
1. (a) List all elements in H=<9>, viewed as a cyclic subgroup of Z30
(b) Find all z in H such that H=<z>
I'm thinking that H=<9> = {1,7,9} (viewed as a cyclic subgroup of Z30) is this correct?
And could someone explain what (b) is asking in other terms?
(A) Let (G,*) be a group such that x*x=e[SIZE="1"]G for all x in G. Prove G is commutative.
(B) Give a specific example of an infinite group (G,*) such that x*x=e[SIZE="1"]G for all x in G.
I have not gotten very far, just to let two variable x,y be in G and I know that (x*y)*(x*y) =...