Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $G$ be a group and let $G_n$ be its series of dimension subgroups defined as follows:

$$G_n=\{g \in G | g-1 \in \Delta\} $$ where $\Delta$ is the augmentation ideal.

This series has the property $[G_m,G_n]\leq G_{m+n}$. If $G_n/G_{n+1}$ are elementary abelian p groups It follows that $$ L(G)= \bigoplus (G_n/G_{n+1}) $$ forms a Lie algebra over $F_p$.

In a paper I am reading it is said that $L(G)$ and $L(\hat G)$ are isomorphic. (The group in consideration is a 2 group). Does this follow easily from the definitions? If not could you give me a reference for this?

Thanks in advance

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.