Identify the kernel and whether or not the following mapping is 1-1 or onto
1. G group, φ: G-> G defined by φ(a) = a^-1 for a is an element of G
How can I find out if a homomorphism is 1-1 or onto
Thanks
1-1 and onto are two separate concepts, so there is no 'or' concept here.
for 1-1: Show if φ(g1) = φ(g2) then g1=g2. This is very easy in this problem
for onto: Show for ever g in G, there is an h in G such that φ(h) = g. This is again easy here as it follows directly from Group Axioms