Flexibility in generating sets of finite groups
- Resource Type
- Authors
- Scott Harper
- Source
- Harper, S 2022, ' Flexibility in generating sets of finite groups ', Archiv der Mathematik, vol. 118, no. 3, pp. 231–237 . https://doi.org/10.1007/s00013-021-01691-0
- Subject
- Spread
General Mathematics
T-NDAS
Generating sets
Bases
FOS: Mathematics
Finite grouops
Group Theory (math.GR)
Finite groups
Mathematics - Group Theory
- Language
- ISSN
- 1420-8938
0003-889X
Let G be a finite group. It has recently been proved that every nontrivial element of G is contained in a generating set of minimal size if and only if all proper quotients of G require fewer generators than G. It is natural to ask which finite groups, in addition, have the property that any two elements of G that do not generate a cyclic group can be extended to a generating set of minimal size. This note answers the question. The only such finite groups are very specific affine groups: elementary abelian groups extended by a cyclic group acting as scalars.
5 pages; to appear in Archiv der Mathematik