Finite class 2 nilpotent and Heisenberg groups
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Dávid R. Szabó
Abstract
We present a structural description of finite nilpotent groups of class at most 2 using a specified number of subdirect and central products of such groups that are 2-generated. As a corollary, we show that any such group is isomorphic to a subgroup of a Heisenberg group satisfying certain properties. The motivation for these results is of a topological nature as they can be used to give lower bounds to the nilpotently Jordan property of the birational automorphism group of varieties and the homeomorphism group of compact manifolds.
Funding source: Horizon 2020 Framework Programme
Award Identifier / Grant number: 741420
Funding source: National Research, Development and Innovation Office
Award Identifier / Grant number: K138596
Funding statement: The project leading to this application has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 741420). The author was supported by the National Research, Development and Innovation Office (NKFIH) Grant K138596.
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Communicated by: Bettina Eick
References
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Articles in the same Issue
- Frontmatter
- Bounding the degree of generic sharp transitivity
- Structure of an exotic 2-local subgroup in 𝐸7(𝑞)
- Set-stabilizers in solvable permutation groups
- Regular saturated formations of finite soluble groups
- On the 𝑝-length and 𝔘-class of a 𝑝-solvable finite group
- Finite 2-groups with exactly three automorphism orbits
- Finite class 2 nilpotent and Heisenberg groups
- Minimal degrees for faithful permutation representations of groups of order 𝑝5 where 𝑝 is an odd prime
- 𝜏-Tilting finiteness of group algebras of semidirect products of abelian 𝑝-groups and abelian 𝑝′-groups
- On the Grossman representations of the automorphism groups of free groups
- Strong indecomposability of the outer automorphism groups of nonabelian free profinite groups
- The proper geometric dimension of the mapping class group of an orientable surface with punctures
- A note on complex hyperbolic lattices and strict hyperbolization
Articles in the same Issue
- Frontmatter
- Bounding the degree of generic sharp transitivity
- Structure of an exotic 2-local subgroup in 𝐸7(𝑞)
- Set-stabilizers in solvable permutation groups
- Regular saturated formations of finite soluble groups
- On the 𝑝-length and 𝔘-class of a 𝑝-solvable finite group
- Finite 2-groups with exactly three automorphism orbits
- Finite class 2 nilpotent and Heisenberg groups
- Minimal degrees for faithful permutation representations of groups of order 𝑝5 where 𝑝 is an odd prime
- 𝜏-Tilting finiteness of group algebras of semidirect products of abelian 𝑝-groups and abelian 𝑝′-groups
- On the Grossman representations of the automorphism groups of free groups
- Strong indecomposability of the outer automorphism groups of nonabelian free profinite groups
- The proper geometric dimension of the mapping class group of an orientable surface with punctures
- A note on complex hyperbolic lattices and strict hyperbolization
