Suzuki2B2 - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim


GroupTheory

  

Suzuki2B2

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Suzuki2B2( q )

Parameters

q

-

: {posint,algebraic} : an odd power of , or an expression

Description

• 

The Suzuki groups  , of type , for an odd power  of , are a series of (typically) simple groups of Lie type, first constructed by M. Suzuki. They are defined only for  an odd power of  (where, here, ).

• 

The groups  should not be confused with the "Suzuki group" of order , one of the sporadic finite simple groups. (See GroupTheory[SuzukiGroup].)

• 

The Suzuki groups  are notable among the finite simple groups in that they are the only finite non-abelian simple groups whose order is not divisible by .

• 

The Suzuki2B2( q ) command constructs a permutation group isomorphic to  , for admissible values of  up to .

• 

If the argument q is not numeric, or if it is an odd power of  greater than , then a symbolic group representing  is returned.

  

(The Suzuki groups  and  are also available by using the ExceptionalGroup command.)

Examples

The smallest of the Suzuki groups is a non-simple group of order  that is, in fact, a soluble Frobenius group.

(1)

(2)

(3)

(4)

(5)

(6)

For values of  larger than , the group  is simple.

(7)

(8)

(9)

(10)

(11)

C

1a

2a

4a

4b

5a

7a

7b

7c

13a

13b

13c

|C|

1

455

1820

1820

5824

4160

4160

4160

2240

2240

2240

 

 

 

 

 

 

 

 

 

 

 

 

For non-numeric arguments, a symbolic group is returned.

(12)

(13)

(14)

(15)

A symbolic group is also returned if the numeric argument q exceeds .

(16)

(17)

(18)

(19)

Compatibility

• 

The GroupTheory[Suzuki2B2] command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

GroupTheory

GroupTheory[ExceptionalGroup]

GroupTheory[GroupOrder]

GroupTheory[IsCNGroup]

GroupTheory[IsFrobenius]

GroupTheory[IsSimple]

GroupTheory[SuzukiGroup]

 


Download Help Document