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,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hul...@math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke
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