- #1

catherinenanc

- 49

- 0

**1. Let G be any group and x∈G. Let σ be the map σ:y→xyx⁻¹. Prove that this map is bijective.**

It seems to be written strangely, since it never really says anywhere that y is in G, but I guess that must be an assumption.

**2. bijective=injective+surjective.**

in order to prove injective, we need to show that y1≠y2→xy1x⁻¹≠xy2x⁻¹

and in order to prove surjective, we need to show that for every g in G, there exists a y in G such that xyx^-1=g.

in order to prove injective, we need to show that y1≠y2→xy1x⁻¹≠xy2x⁻¹

and in order to prove surjective, we need to show that for every g in G, there exists a y in G such that xyx^-1=g.

**3. I think that I can say: Let y=x^-1gx. Then xyx-1=g and we are done for surjective.**

I don't really know how to "show" injective, since it seems obvious.

I don't really know how to "show" injective, since it seems obvious.