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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.

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  • $\begingroup$ This is just a guess, but perhaps they mean the centralizer of the centralizer. $\endgroup$ Apr 1 '16 at 0:16
  • $\begingroup$ Thnx. May be, but is there any article or literature from where I can get the information about the definition? $\endgroup$
    – usermath
    Apr 1 '16 at 0:18
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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 $\gamma_i(G)/\gamma_{i+2}(G)$.

See "The Structure of Groups of Prime Power Order" Definition 3.1.3.

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