Normal subgroups of iterated wreath products of symmetric groups and alternating with symmetric groups

Publication date: 8 August 2021

Abstract: Normal subgroups and there properties for finite and infinite iterated wreath products

S_{n_{1}} w r l d o t s w r S_{n_{m}}

,

n, m i n m a t h b b N

are founded. The special classes of normal subgroups and there orders are investigated. Special classes of normal subgroups are investigated and their generators are found and presented in the form of Kaloujnine tables. Inverse limit of wreath product of permutation groups is found.

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Maximal subgroups (20E28) Generators, relations, and presentations of groups (20F05) General theory for infinite permutation groups (20B07) Groups acting on trees (20E08) Subgroups of symmetric groups (20B35) General theory for finite permutation groups (20B05) Multiply transitive infinite groups (20B22)

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