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Zbl 0714.11075
Pahlings, H.
Some sporadic groups as Galois groups. II. (English)
[J] Rend. Semin. Mat. Univ. Padova 82, 163-171 (1989). ISSN 0041-8994

[For part I, cf. Rend. Semin. Mat. Univ. Padova 79, 97-107 (1988; Zbl 0663.12013)]. \par It is proved that the sporadic simple groups $J\sb 3$, McL, Ru and Ly as well as their automorphism groups are Galois groups over ${\bbfQ}(T)$. The author shows that these groups have a GAR-realization over ${\bbfQ}(T)$, using {\it B. H. Matzat}'s criterion [Invent. Math. 80, 365-374 (1985; Zbl 0567.12015)]. Summarizing previous results of Hoyden- Siedersleben, Hunt, Matzat and the author it is obtained that all sporadic simple groups, except the Mathieu group $M\sb{23}$, are Galois groups of regular extensions of ${\bbfQ}(T)$.
[N.Vila]

MSC 2000:: *11R32 Galois theory for global fields
12F12 Inverse Galois theory
20D08 Simple groups: sporadic finite groups
20F29 Representations of groups as automorphism groups of alg. systems
11R58 Arithmetic theory of algebraic function fields

Keywords: inverse Galois problem; sporadic simple groups; Galois groups; regular extensions

Citations: Zbl 0663.12013; Zbl 0567.12015

Cited in: Zbl 0748.11055

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