[GAP Forum] Forum Digest, Vol 86, Issue 6

[Alexander Hulpke]

Dear Forum,

> Let the set of the number of sylow subgroup $G$ equal to group $PSL(2,7)$
> (that is {8,21,28}) .Whether by GAP we can say $G$ is solvable group
> or unsolvable group?

This is a question that is not really suitable for computer analysis -- clearly the answer is known and is `unsolvable'.

You might want to look in the book
Abstract Algebra by Dummit and Foote 
I believe they show uniqueness of L3(2) as a simple group of order 168.

Best,

   Alexander Hulpke



-- Colorado State University, Department of Mathematics,
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