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Questions about the branch of algebra that deals with groups.

4 votes
3 answers
625 views

Group PGL(2,p) where p is prime

Is there solvable group $G$ such that prime graph $G$ equal to prime graph $PGL(2,p)$ and $|G|=|PSL(2,p)|$?
5 votes
3 answers
645 views

Reference request for the number of Sylow p-subgroups

Let $G$ be simple group of Lie type or Alternating group. I need reference for find the number of Sylow $p$-subgroup $G$ for every $p$. Thanks a lot.
13 votes
2 answers
767 views

The prime divisors of a simple group

Let $G$ be a finite simple group such that $\pi (G)=\pi (A_{n})$, where $n\geq 23$ ($\pi (G)$ is the set of prime divisors of the order of $G$). Is it true that $G$ is isomorphic to an alternating gro …