Elementary Abelian Group of Order 9

Elementary Abelian Group of order 9 White Sheet [Printable Version]

Subgroup Lattice Element Lattice

Alternate Descriptions: (* Most common)

Name Symbol(s)

Abelian [3,3] * C3 x C3,
Z3 x Z3

Elementary Abelian EA(9)

GAP ID: [9,2]
Magma ID:?

Standard Invariants:

Invariant Value

Abelian True

Nilpotent True

Nilpotency Class 1

Ascending Central Series [0, C3 x C3]

Descending Central Series [C3 x C3, 0]

Solvable True

Composition Factors {C3, C3}

Automorphism Group GL2(3)

Name	Symbol(s)
Abelian [3,3]	* C3 x C3, Z3 x Z3
Elementary Abelian	EA(9)

Invariant	Value
Abelian	True
Nilpotent	True
Nilpotency Class	1
Ascending Central Series	[0, C3 x C3]
Descending Central Series	[C3 x C3, 0]
Solvable	True
Composition Factors	{C3, C3}
Automorphism Group	GL2(3)