Realizing finite groups as automizers
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Sylvia Bayard
Abstract
It is shown that any finite group 𝐴 is realizable as the automizer in a finite perfect group 𝐺 of an abelian subgroup whose conjugates generate 𝐺. The construction uses techniques from fusion systems on arbitrary finite groups, most notably certain realization results for fusion systems of the type studied originally by Park.
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1902152
Funding statement: J. Lynd was partially supported by NSF Grant DMS-1902152.
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Communicated by: Christopher W. Parker
References
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Multiple transitivity except for a system of imprimitivity
- Realizing finite groups as automizers
- Action of automorphisms on irreducible characters of finite reductive groups of type 𝖠
- Polynomial maps and polynomial sequences in groups
- Units, zero-divisors and idempotents in rings graded by torsion-free groups
- The algebraic entropy of one-dimensional finitary linear cellular automata
- Sublinearly Morse boundary of CAT(0) admissible groups
Artikel in diesem Heft
- Frontmatter
- Multiple transitivity except for a system of imprimitivity
- Realizing finite groups as automizers
- Action of automorphisms on irreducible characters of finite reductive groups of type 𝖠
- Polynomial maps and polynomial sequences in groups
- Units, zero-divisors and idempotents in rings graded by torsion-free groups
- The algebraic entropy of one-dimensional finitary linear cellular automata
- Sublinearly Morse boundary of CAT(0) admissible groups
