GroupTheory
SylowSubgroup
construct a Sylow subgroup of a group
Calling Sequence
Parameters
Description
Examples
Compatibility
SylowSubgroup( p, G )
p
-
a positive rational prime
G
a permutation group or Cayley table group
Let be a finite group, and let be a positive (rational) prime. A Sylow -subgroup of is a maximal -subgroup of where, by a -subgroup, we mean a subgroup whose order is a power of . The Sylow theorems assert that, for a prime divisor of the order of a finite group , there is a Sylow -subgroup of and that all Sylow -subgroups of are conjugate in . Moreover, the number of Sylow -subgroups of is congruent to modulo .
The SylowSubgroup( p, G ) command constructs a Sylow p-subgroup of a group G. The group G must be an instance of a permutation group or a Cayley table group.
Note that, if p is not a divisor of the order of G, then the trivial subgroup of G is returned.
The GroupTheory[SylowSubgroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
See Also
GroupTheory[AlternatingGroup]
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