Geodesic
The size of the solvable residual in finite groups
Silvio Dolfi1 ; Marcel Herzog2 ; Gil Kaplan3 ; Arieh Lev4
1Università degli Studi di Firenze, Italy
2Tel Aviv University, Israel
3The Academic College of Tel Aviv-Yaffo, Israel
4The Academic College of Tel-Aviv-Yaffo, Israel
Groups, geometry, and dynamics, Tome 1 (2007) no. 4, pp. 401-407

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DOI

Let G be a finite group. The solvable residual of G, denoted by Res(G), is the smallest normal subgroup of G such that the respective quotient is solvable. We prove that every finite non-trivial group G with a trivial Fitting subgroup satisfies the inequality ∣Res(G)∣ > ∣G∣β, where β=log(60)/log(120(24)1/3) ≈ 0.700265861. The constant β in this inequality can not be replaced by a larger constant.
DOI : 10.4171/ggd/19
Classification : 20-XX, 00-XX
Mots-clés : Commutator subgroup, centre, Frattini subgroup, Fitting subgroup, solvable residual

Silvio Dolfi  1   ; Marcel Herzog  2   ; Gil Kaplan  3   ; Arieh Lev  4

1 Università degli Studi di Firenze, Italy
2 Tel Aviv University, Israel
3 The Academic College of Tel Aviv-Yaffo, Israel
4 The Academic College of Tel-Aviv-Yaffo, Israel 
Silvio Dolfi; Marcel Herzog; Gil Kaplan; Arieh Lev. The size of the solvable residual in finite groups. Groups, geometry, and dynamics, Tome 1 (2007) no. 4, pp. 401-407. doi: 10.4171/ggd/19
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