GroupTheory
IsElementary
attempt to determine whether a group is elementary Abelian
Calling Sequence
Parameters
Description
Examples
Compatibility
IsElementary( G )
G
-
a finite group
A group G is elementary if it is a finite Abelian group with prime exponent. Equivalently, G is elementary if it is a direct sum (product) of groups each of order equal to a fixed prime p.
The IsElementary( G ) command attempts to determine whether the group G is elementary. It returns true if G is elementary and returns false otherwise.
The group G must be an instance of a permutation group, a Cayley table group or a finite, finitely presented group.
withGroupTheory:
G≔SmallGroup32,1:
IsElementaryG
false
G≔SmallGroup17,1:
true
IsElementaryDirectProduct`$`CyclicGroup2,5
IsElementaryWreathProduct`$`CyclicGroup2,5
G≔CayleyTableGroup1|2|3|4,2|1|4|3,3|4|1|2,4|3|2|1
G≔ < a Cayley table group with 4 elements >
G≔CayleyTableGroup1|2|3|4|5|6,2|1|4|3|6|5,3|5|1|6|2|4,4|6|2|5|1|3,5|3|6|1|4|2,6|4|5|2|3|1
G≔ < a Cayley table group with 6 elements >
IsElementarya,b,c|a5,b5,c5,a·b=b·a,a·c=c·a,b·c=c·b
The GroupTheory[IsElementary] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
See Also
GroupTheory[IsAbelian]
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