# Invariable generation of permutation and linear groups

Research output: Contribution to journalArticle

### Abstract

A subset {x 1,x 2,…,x d} of a group G invariably generates G if {x 1 g 1 ,x 2 g 2 ,…,x d g d } generates G for every d-tuple (g 1,g 2…,g d)∈G d. We prove that a finite completely reducible linear group of dimension n can be invariably generated by ⌊[Formula presented]⌋ elements. We also prove tighter bounds when the field in question has order 2 or 3. Finally, we prove that a transitive [respectively primitive] permutation group of degree n≥2 [resp. n≥3] can be invariably generated by O([Formula presented]) [resp. O([Formula presented])] elements.

Original language English 250-289 40 Journal of Algebra 524 4 Feb 2019 https://doi.org/10.1016/j.jalgebra.2019.01.018 Published - 15 Apr 2019

### Keywords

• Conjugation properties in finite groups
• Generation of finite groups

### ASJC Scopus subject areas

• Algebra and Number Theory

### Cite this

In: Journal of Algebra, Vol. 524, 15.04.2019, p. 250-289.

Research output: Contribution to journalArticle

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