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- Title
Minimal orbit sizes in nilpotent group actions.
- Authors
Keller, Thomas Michael; Lv, Heng; Qian, Guohua; Yang, Dongfang
- Abstract
Let G be a finite nilpotent group. We prove the following results. (1) If G is of class 2 and acts faithfully and irreducibly on an elementary abelian group V , then all nontrivial orbits of G on V have sizes larger than | G | 1 / 2 . (2) If G ′ is cyclic, then every subgroup of G intersecting trivially with the center of G has order less than | G | 1 / 2 . We also show that a result like (2) cannot be obtained when the hypothesis that G ′ is cyclic is replaced by the hypothesis that the center of G is cyclic.
- Subjects
NILPOTENT groups; ORBITS (Astronomy); ABELIAN groups; FINITE groups
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 7, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823501530