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Results tagged with nilpotent-groups
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user 801
7
votes
Accepted
Why do we say the Fitting subgroup/generalized Fitting subgroup control the structure of a g...
I'll try and give my point of view on the question in the title.
The key facts that answer your question are the following:
If $G$ is a finite solvable group, then $C_G(F(G))=Z(F(G))$.
If $G$ is a …
- 11.2k
7
votes
Accepted
element of order n such that $\pi(n)=\pi(G)$, where $\pi(n)$ denote the prime divisors of $n$
There is a pathological example that pretty much demonstrates that the existence of such an element gives no significant information about the group:
Example 1. Let $H$ be any finite group, and le …
- 11.2k