GroupTheory
Exponent
compute the exponent of a finite group
Calling Sequence
Parameters
Description
Examples
Compatibility
Exponent(G)
G
-
a permutation group or a Cayley table group
The exponent of a finite group G is the least positive integer e such that g^e = 1, for all g in G. It is equal to the least common multiple of the orders of the elements of G, and is a divisor of the order of G.
The Exponent(G) command computes the exponent of the finite group G, if possible.
Note that the exponent of a finite finitely presented group can be computed by first converting it to a permutation group using the PermutationGroup command.
with⁡GroupTheory:
G≔SymmetricGroup⁡5
G≔S5
Exponent⁡G
60
Exponent⁡ElementaryGroup⁡7,3
7
Exponent⁡QuasicyclicGroup⁡2
∞
G≔a,b|a2,b3,a·b5=1
G≔⁢a,b⁢∣⁢a2,b3,a⁢b⁢a⁢b⁢a⁢b⁢a⁢b⁢a⁢b⁢
Error, (in Exponent) cannot compute the Exponent of a general finitely presented group. If you know that your group is finite, try converting it to a permutation group by using the `PermutationGroup' command with your finitely presented group as input.
Exponent⁡PermutationGroup⁡G
30
The GroupTheory[Exponent] command was introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
See Also
GroupTheory[ElementaryGroup]
GroupTheory[GroupOrder]
GroupTheory[PermutationGroup]
GroupTheory[SymmetricGroup]
with
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