Minimal length factorizations of finite simple groups of Lie type by unipotent Sylow subgroups
-
Martino Garonzi
,
Dan Levy
Abstract
We prove that every finite simple group G of Lie type satisfies G = UU-UU-, where U is a unipotent Sylow subgroup of G and U- is its opposite. We also characterize the cases for which G = UU-U. These results are best possible in terms of the number of conjugates of U in the above factorizations.
Funding source: MIUR
Award Identifier / Grant number: PRIN Group theory and applications
Funding source: Alexander von Humboldt Fellowship for Experienced Researchers
Funding source: MTA
Award Identifier / Grant number: Rényi "left Lendület” Groups and Graphs Research Group
Funding source: OTKA
Award Identifier / Grant number: K84233
Funding source: University of Padova
Award Identifier / Grant number: CPDR131579/13
Funding source: University of Padova
Award Identifier / Grant number: CPDA125818/12
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Mapping tori of free group automorphisms, and the Bieri–Neumann–Strebel invariant of graphs of groups
- Residual properties of graph products of groups
- On hereditarily just infinite profinite groups obtained via iterated wreath products
- Weak commutativity between two isomorphic polycyclic groups
- Isomorphisms and automorphisms of extensions of bilinear dimensional dual hyperovals and quadratic APN functions
- Finite groups in which pronormality and 𝔉-pronormality coincide
- Towards Thompson's conjecture for alternating and symmetric groups
- Minimal length factorizations of finite simple groups of Lie type by unipotent Sylow subgroups
- A criterion for a finite permutation group to be transitive
- Inverse Glauberman–Isaacs correspondence and subnormal subgroups
Articles in the same Issue
- Frontmatter
- Mapping tori of free group automorphisms, and the Bieri–Neumann–Strebel invariant of graphs of groups
- Residual properties of graph products of groups
- On hereditarily just infinite profinite groups obtained via iterated wreath products
- Weak commutativity between two isomorphic polycyclic groups
- Isomorphisms and automorphisms of extensions of bilinear dimensional dual hyperovals and quadratic APN functions
- Finite groups in which pronormality and 𝔉-pronormality coincide
- Towards Thompson's conjecture for alternating and symmetric groups
- Minimal length factorizations of finite simple groups of Lie type by unipotent Sylow subgroups
- A criterion for a finite permutation group to be transitive
- Inverse Glauberman–Isaacs correspondence and subnormal subgroups
