FiSGO.OrderSearch.simple_group_by_order

simple_group_by_order(prime_bounds, abs_bound=None, return_codes=True, ignore=None)[source]

Returns a list of all simple groups whose order divides prime_bounds and is less than or equal to abs_bound.

Certain groups can be ignored by providing a list of ids to ignore. See FiSGO.SimpleGroups.simple_group_ids() for a list of valid ids. By default, no groups are ignored.

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.

  • 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 FiSGO.SimpleGroups.simple_group_ids().

  • ignore (list[str] | None) – List of groups to ignore given as a list of code ids, example: [‘AA’, ‘SP’]. For all ids see FiSGO.SimpleGroups.simple_group_ids(). By default, no groups are ignored.

Return type:

list[str | SimpleGroup]

Returns:

A list of simple groups (objects or codes depending on ‘return_codes’) free of duplicates.