wreath product of symmetric groups

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept group theory concept
gptkbp:application	gptkb:Galois_theory combinatorics 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	direct product of symmetric groups semidirect product
gptkbp:hasSubgroup	gptkb:group_of_people direct product of symmetric groups
https://www.w3.org/2000/01/rdf-schema#label	wreath 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 wreath product
gptkbp:seeAlso	permutation group wreath product
gptkbp:usedIn	construction of imprimitive permutation groups
gptkbp:bfsParent	gptkb:Hamming_graph
gptkbp:bfsLayer	5