Info_Files

For the translation planes of order 49=7^2 the following
files are available:


49_spreadsetsGAP:

- This file uses GAP notation. It contains a set "spreadsets" of
  spread sets "spreadsets[1..N]" with "N:=Size( spreadsets )=973".
  Each set spreadsets[i] consists of 48 matrices "spreadsets[i][j]"
  which lie in GL(2,7). 


49_matgenGAP:

- This file uses GAP notation. It contains a set "matgen" of
  sets "matgen[1..N]" and each set "matgen[i]" consists of matrices
  "matgen[i][[1..M]" in GL(4,7) with "M:=Size( matgen[i] )". 
  The group "G:= Group( matgen[i] )" generated by  matgen[i]
  is the stabilizer of the spread associated with spreadsets[i] 
  in GL(4,7), i.e. G is isomorphic to a translation complement.


49_permGAP: 

- This file uses GAP notation. It contains a set "permgen" of
  sets "permgen[1..N]" and each set "permgen[i]" consists of permutations
  "permgen[i][[1..M]"  in Sym(50) with "M:=Size( permgen[i] )".  
  The group "H:= Group( permgen[i] )"  generated by  permgen[i]
  is the group induced by G (= Group( matgen[i] ) ) on the line at infinity.


49_Data:

- This is a GAP output file. It displays:

  1. The number of a spread in spreadsets. 
  2. The order of the translation complement, i.e. |G|.
  3. The order of the kernel of the spread.
  4. "true" or "false" according as to whether or not G is solvable. 
  5. The order of the group H induced by G on the line at infinity.
  6. The orbit lengths of H on the line at infinity.

49_pol: 

- There are 1347 translation planes but only 973 spread sets are
  displayed. It can happen that a spread set S is not equivalent
  to the spread set S^t, where the matrices of S^t are the transposed
  matrices of S. In this case only one spread set is shown. This file
  has the entry "polar" if the two sets S and S^t are equivalent and the
  entry "unpolar" otherwise.
     

49_spreadsetsZ_7:

- This file has the same content as 49_spreadsetsGAP. However matrices
  have entries from [0..6].

49_matgenZ_7:

- This file has the same content as 49_matgenGAP. However matrices
  have entries from [0..6].