# Definition of two step centraliser

I was reading few topics related to p groups and pro p groups. Then I came across the term "two step centraliser". I could not find the definition of this in google search.

It will be very helpful for me if someone give me some idea and related links for the definition. I will be grateful. Thnx in advance.

I am sorry for this kind of simple question, perhaps I missed something. I am really sorry. Please help me. Thanks again.

• This is just a guess, but perhaps they mean the centralizer of the centralizer. Apr 1 '16 at 0:16
• Thnx. May be, but is there any article or literature from where I can get the information about the definition? Apr 1 '16 at 0:18

Let $$G$$ be a finite group. Define $$\gamma_2(G) = [G, G]$$ and $$\gamma_{i+1}(G) = [\gamma_i(G), G]$$ for all $$i \geq 2$$.
Let $$G$$ be a finite $$p$$-group. For each $$i$$ with $$2 \leq i \leq n-2$$, the 2-step centralizer $$K_i$$ in $$G$$ is defined to be the centralizer in $$G$$ of $$\gamma_i(G)/\gamma_{i+2}(G)$$.