test whether a finite magma is a group - Maple Help

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Magma[IsGroup] - test whether a finite magma is a group

Calling Sequence

IsGroup( m )

Parameters

m

-

Array representing the Cayley table of a finite magma

Description

• 

The IsGroup command returns true if the given magma is a group, and returns false otherwise.

• 

A group is an associative magma with an identity element, with respect to which identity each member has a (two-sided) inverse. Alternatively, a group is an associative loop.

Examples

withMagma:

m:=1|2|3,2|3|1,3|1|2

m:=123231312

(1)

IsGroupm

true

(2)

m:=1|2|3,2|3|3,3|1|2

m:=123233312

(3)

IsGroupm

false

(4)

See Also

IsLoop, IsMonoid, Magma


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