Base class for groups¶
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class
sage.groups.group.
AbelianGroup
¶ Bases:
sage.groups.group.Group
Generic abelian group.
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is_abelian
()¶ Return True.
EXAMPLES:
sage: from sage.groups.group import AbelianGroup sage: G = AbelianGroup() sage: G.is_abelian() True
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class
sage.groups.group.
AlgebraicGroup
¶ Bases:
sage.groups.group.Group
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class
sage.groups.group.
FiniteGroup
¶ Bases:
sage.groups.group.Group
Generic finite group.
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is_finite
()¶ Return
True
.EXAMPLES:
sage: from sage.groups.group import FiniteGroup sage: G = FiniteGroup() sage: G.is_finite() True
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class
sage.groups.group.
Group
¶ Bases:
sage.structure.parent.Parent
Base class for all groups
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is_abelian
()¶ Test whether this group is abelian.
EXAMPLES:
sage: from sage.groups.group import Group sage: G = Group() sage: G.is_abelian() Traceback (most recent call last): ... NotImplementedError
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is_commutative
()¶ Test whether this group is commutative.
This is an alias for is_abelian, largely to make groups work well with the Factorization class.
(Note for developers: Derived classes should override is_abelian, not is_commutative.)
EXAMPLES:
sage: SL(2, 7).is_commutative() False
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is_finite
()¶ Returns True if this group is finite.
EXAMPLES:
sage: from sage.groups.group import Group sage: G = Group() sage: G.is_finite() Traceback (most recent call last): ... NotImplementedError
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is_multiplicative
()¶ Returns True if the group operation is given by * (rather than +).
Override for additive groups.
EXAMPLES:
sage: from sage.groups.group import Group sage: G = Group() sage: G.is_multiplicative() True
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order
()¶ Return the number of elements of this group.
This is either a positive integer or infinity.
EXAMPLES:
sage: from sage.groups.group import Group sage: G = Group() sage: G.order() Traceback (most recent call last): ... NotImplementedError
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quotient
(H, **kwds)¶ Return the quotient of this group by the normal subgroup \(H\).
EXAMPLES:
sage: from sage.groups.group import Group sage: G = Group() sage: G.quotient(G) Traceback (most recent call last): ... NotImplementedError
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sage.groups.group.
is_Group
(x)¶ Return whether
x
is a group object.INPUT:
x
– anything.
OUTPUT:
Boolean.
EXAMPLES:
sage: F.<a,b> = FreeGroup() sage: from sage.groups.group import is_Group sage: is_Group(F) True sage: is_Group("a string") False