Projective special linear group:PSL(3,9)
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- It is the projective special linear group of degree three over field:F9, denoted .
- It is the special linear group of degree three over field:F9, denoted .
- It is the projective general linear group of degree three over field:F9, denoted .
Equivalence of definitions
The equivalence of definitions follows from isomorphism between linear groups when degree power map is bijective.
Basic arithmetic functions
|order (number of elements, equivalently, cardinality or size of underlying set)||42456960||groups with same order||As :|
|exponent of a group||21840||groups with same order and exponent of a group | groups with same exponent of a group|
|Frattini length||1||groups with same order and Frattini length | groups with same Frattini length||As the group is a simple non-abelian group, its Frattini length must be one.|
|simple group, simple non-abelian group||Yes||projective special linear group is simple|
|minimal simple group||No||contains projective special linear group:PSL(3,3). See classification of finite minimal simple groups.|