Direct product of Z4 and Z4

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VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

This group is defined in the following equivalent ways:

• It is a homocyclic group of order sixteen and exponent four.
• It is the direct product of two copies of cyclic group:Z4.

Arithmetic functions

Function	Value	Explanation
order	16
exponent	4
nilpotency class	1
derived length	1
Frattini length	2
Fitting length	1
minimum size of generating set	2
subgroup rank	2
rank	2
normal rank	2
characteristic rank	2

Group properties

Property	Satisfied	Explanation	Comment
Abelian group	Yes	Direct product of cyclic groups
Nilpotent group	Yes	Abelian implies nilpotent
Metacyclic group	Yes
Supersolvable group	Yes
Solvable group	Yes