- #1
Punkyc7
- 420
- 0
Let H be a subgroup of G and define the core of H as such
core H={g[itex]\in[/itex]G| g[itex]\in[/itex]aHa^-1 for all a[itex]\in[/itex]G}= [itex]\bigcap[/itex]{aHa^-1|a[itex]\in[/itex]G}
Prove that the core of H is normal in G and core H[itex]\subset[/itex]H.
I am having a hard time proving this because isn't the definition of core H basically saying the the core is normal?
core H={g[itex]\in[/itex]G| g[itex]\in[/itex]aHa^-1 for all a[itex]\in[/itex]G}= [itex]\bigcap[/itex]{aHa^-1|a[itex]\in[/itex]G}
Prove that the core of H is normal in G and core H[itex]\subset[/itex]H.
I am having a hard time proving this because isn't the definition of core H basically saying the the core is normal?