10.1 Base class for all groups

Module: sage.groups.group

Class: AbelianGroup

class AbelianGroup
Generic abelian group.

Functions: is_abelian

is_abelian( self)

Return True.

Class: AlgebraicGroup

class AlgebraicGroup
Generic algebraic group.

Class: FiniteGroup

class FiniteGroup
Generic finite group.

Functions: is_finite

is_finite( self)

Return True.

Class: Group

class Group
Generic group class

Functions: category,$  $ is_abelian,$  $ is_atomic_repr,$  $ is_finite,$  $ order,$  $ quotient,$  $ random_element

category( self)

The category of all groups

is_abelian( self)

Return True if this group is abelian.

is_atomic_repr( self)

True if the elements of this group have atomic string representations. For example, integers are atomic but polynomials are not.

is_finite( self)

Returns True if this group is finite.

order( self)

Returns the number of elements of this group, which is either a positive integer or infinity.

quotient( self, H)

Return the quotient of this group by the normal subgroup $ H$ .

random_element( self, bound=None)

Return a random element of this group.

Special Functions: __call__,$  $ __contains__,$  $ _coerce_

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