FiSGO.OrderSearch.candidates_exceptional_chevalley

candidates_exceptional_chevalley(prime_bounds, abs_bound, q_power, product_indices, gcd_value, group_id, return_codes)[source]

Generic function with the procedure to find exceptional Chevalley groups whose order divides prime_bounds and is less than or equal to abs_bound.

To understand the parameters refering to the group order, see the order table in Wikipedia.

Parameters:

  • prime_bounds (list[int]) – Contains a list with the maximum powers for each prime, example: [2,0,1,0,3] means the order of the group must divide 2^2*5^1*11^3.

  • abs_bound (int | None) – An integer providing an upper bound to the order of the group, if None, then it is constructed from prime_bounds.

  • q_power (int) – Exponent of the q factor in the group order.

  • product_indices (list[int]) – Indices of the capital Pi notation in the group order.

  • gcd_value (int) – In the group order, number corresponding to gcd(gcd_value, q-1).

  • group_id (str) – The ID of the exceptional Chevalley group.

  • return_codes (bool) – If False, the function returns a list of derived objects from the SimpleGroup class. If True, the function returns a list of strings, each string represents a simple group code. See SimpleGroups.simple_group_ids.

Returns:

Returns a list, the contents depend on the return_codes parameter.