Cyclic group:Z128
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Contents
Definition
This group is defined as the cyclic group of order , denoted
,
, or
.
Arithmetic functions
Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 128#Arithmetic functions
GAP implementation
Group ID
This finite group has order 128 and has ID 1 among the groups of order 128 in GAP's SmallGroup library. For context, there are groups of order 128. It can thus be defined using GAP's SmallGroup function as:
SmallGroup(128,1)
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(128,1);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [128,1]
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 | Mathematical comments |
---|---|---|
CyclicGroup(128) | CyclicGroup |