Nilpotent, Abelian and Cyclic Numbers#
- sympy.combinatorics.group_numbers.is_nilpotent_number(n)[source]#
Check whether \(n\) is a nilpotent number. A number \(n\) is said to be nilpotent if and only if every finite group of order \(n\) is nilpotent. For more information see [R48].
Examples
>>> from sympy.combinatorics.group_numbers import is_nilpotent_number >>> from sympy import randprime >>> is_nilpotent_number(21) False >>> is_nilpotent_number(randprime(1, 30)**12) True
References
- sympy.combinatorics.group_numbers.is_abelian_number(n)[source]#
Check whether \(n\) is an abelian number. A number \(n\) is said to be abelian if and only if every finite group of order \(n\) is abelian. For more information see [R49].
Examples
>>> from sympy.combinatorics.group_numbers import is_abelian_number >>> from sympy import randprime >>> is_abelian_number(4) True >>> is_abelian_number(randprime(1, 2000)**2) True >>> is_abelian_number(60) False
References
- sympy.combinatorics.group_numbers.is_cyclic_number(n)[source]#
Check whether \(n\) is a cyclic number. A number \(n\) is said to be cyclic if and only if every finite group of order \(n\) is cyclic. For more information see [R50].
Examples
>>> from sympy.combinatorics.group_numbers import is_cyclic_number >>> from sympy import randprime >>> is_cyclic_number(15) True >>> is_cyclic_number(randprime(1, 2000)**2) False >>> is_cyclic_number(4) False
References