wreath product of symmetric groups
GPTKB entity
Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
gptkb:group_theory_concept |
| gptkbp:application |
gptkb:combinatorics
gptkb:Galois_theory permutation group theory |
| gptkbp:defines |
The wreath product of two symmetric groups S_m and S_n is the semidirect product of the direct product of n copies of S_m with S_n.
|
| gptkbp:field |
abstract algebra
group theory |
| gptkbp:generalizes |
gptkb:semidirect_product
direct product of symmetric groups |
| gptkbp:hasSubgroup |
gptkb:group_of_people
direct product of symmetric groups |
| gptkbp:notation |
S_m wr S_n
|
| gptkbp:order |
(m!)^n n!
|
| gptkbp:property |
finite if m and n are finite
non-abelian for m,n > 2 |
| gptkbp:relatedTo |
gptkb:group_of_people
gptkb:wreath_product |
| gptkbp:seeAlso |
gptkb:permutation_group
gptkb:wreath_product |
| gptkbp:usedIn |
construction of imprimitive permutation groups
|
| gptkbp:bfsParent |
gptkb:Hamming_graph
|
| gptkbp:bfsLayer |
5
|
| http://www.w3.org/2000/01/rdf-schema#label |
wreath product of symmetric groups
|