Cyclic group:Z40
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Definition
This group, denoted ,
, or
, is defined in the following equivalent ways:
- It is the unique (up to isomorphism) cyclic group of order 40, i.e., it is a group of integers modulo n where
.
- It is the external direct product of cyclic group:Z8 and cyclic group:Z5, i.e., is it
.
GAP implementation
Group ID
This finite group has order 40 and has ID 2 among the groups of order 40 in GAP's SmallGroup library. For context, there are groups of order 40. It can thus be defined using GAP's SmallGroup function as:
SmallGroup(40,2)
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(40,2);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [40,2]
or just do:
IdGroup(G)
to have GAP output the group ID, that we can then compare to what we want.
Other descriptions
Description | Functions used |
---|---|
CyclicGroup(40) | CyclicGroup |
DirectProduct(CyclicGroup(8),CyclicGroup(5)) | CyclicGroup, DirectProduct |