Journal of Group Theory· 2026Q2
Generation of iterated wreath products constructed from almost simple groups
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- Q2SCImago
- 2026year
Short summary
A new method constructs iterated wreath products from sequences of almost simple groups and determines the minimum number of generators required for each product.
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Key points
- Introduces a method to construct iterated wreath products (Wi) from sequences of almost simple groups (Gi).
- Defines the iterative construction as Wi+1 = Gi+1 wr Wi using regular actions.
- Determines the minimum number of generators, d(Wi), for each wreath product in the sequence.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract Let G 1 G_{1} , G 2 G_{2} , … be a sequence of almost simple groups and construct a sequence ( W i ) (W_{i}) of wreath products via W 1 = G 1 W_{1}=G_{1} and, for each i > 1 i>1 , W i + 1 = G i + 1 wr W i W_{i+1}=G_{i+1}\mathbin{\mathrm{wr}}W_{i} via the regular action of each G i G_{i} . We determine the minimum number d ( W i ) d(W_{i}) of generators required for each wreath product in this sequence.
The authors' abstract, as published at the source. Journal of Group Theory, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics