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.

  • $\begingroup$ 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

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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.