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- W2963193153 abstract "A subset {x1,x2,…,xd} of a group G invariably generates G if {x1g1,x2g2,…,xdgd} generates G for every d-tuple (g1,g2…,gd)∈Gd. We prove that a finite completely reducible linear group of dimension n can be invariably generated by ⌊3n2⌋ 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(nlogn) [resp. O(lognloglogn)] elements." @default.
- W2963193153 created "2019-07-30" @default.
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- W2963193153 date "2019-04-01" @default.
- W2963193153 modified "2023-09-30" @default.
- W2963193153 title "Invariable generation of permutation and linear groups" @default.
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- W2963193153 doi "https://doi.org/10.1016/j.jalgebra.2019.01.018" @default.
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