Ulrich Meierfrankenfeld
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| Ulrich Meierfrankenfeld | |
|---|---|
| File:Parker Meierfrankenfeld Rowley.jpgParker_Meierfrankenfeld_Rowley.jpg Meierfrankenfeld (center) with Christopher Parker (left) and Peter Rowley (right) at Oberwolfach, 2003 | |
| Born | 21 April 1962 |
| 🏳️ Nationality | German |
| 🎓 Alma mater | University of Bielefeld |
| 💼 Occupation | |
| Known for | Uniqueness of the monster group Classification of finite simple groups |
Ulrich Meierfrankenfeld (born 21 April 1962) is a German mathematician specializing in group theory. He is a professor in the Department of Mathematics at Michigan State University.[1]
Education
Meierfrankenfeld received his Ph.D. from the University of Bielefeld in 1986 under the supervision of Bernd Stellmacher. His dissertation, Eine Lösung des Pushing-up-Problems für eine Klasse endlicher Gruppen (A solution of the pushing-up problem for a class of finite groups), concerned the pushing-up problem in finite group theory.[2]
Career and research
Since the early 1990s, Meierfrankenfeld has been a professor at Michigan State University.[1]
Uniqueness of the Monster group
In 1989, Meierfrankenfeld, together with Robert Griess and Yoav Segev, published the first complete proof of the uniqueness of the monster group, the largest sporadic simple group. Their paper, published in the Annals of Mathematics, demonstrated that any finite group with the same centralizers of involutions as the monster group must be isomorphic to it.[3] Although Simon P. Norton had earlier announced a proof of uniqueness, the details were never published, making the Griess–Meierfrankenfeld–Segev paper the first complete published proof.[4]
Classification of finite simple groups
Meierfrankenfeld is one of the leaders, together with Stellmacher and Gernot Stroth, of what Michael Aschbacher has termed the "third generation" program for the classification of finite simple groups.[5] This program aims to provide a new proof of the classification for groups of characteristic 2 type using the amalgam method, in contrast to the second-generation "revisionist" project led by Daniel Gorenstein, Richard Lyons, and Ronald Solomon.[6][7]
Other contributions
Meierfrankenfeld has also worked on the structure of locally finite groups, finitary linear groups, and the local structure of finite simple groups. With A. A. Ivanov and Sergey Shpectorov, he has studied maximal 2-local subgroups of the monster group and the baby monster group.[8]
Selected publications
- Griess, Robert L. Jr.; Meierfrankenfeld, Ulrich; Segev, Yoav (1989). "A uniqueness proof for the Monster". Annals of Mathematics. Second Series. 130 (3): 567–602. doi:10.2307/1971455. JSTOR 1971455.
- Meierfrankenfeld, Ulrich; Phillips, Richard E.; Puglisi, Orazio (1993). "Locally solvable finitary linear groups". Journal of the London Mathematical Society. Second Series. 47 (1): 31–40. doi:10.1112/jlms/s2-47.1.31.
- Meierfrankenfeld, Ulrich; Stellmacher, Bernd; Stroth, Gernot (2003). "Finite groups of local characteristic p: an overview". Groups, Combinatorics and Geometry (Durham, 2001). World Scientific. pp. 155–192. Search this book on
- Meierfrankenfeld, Ulrich; Parker, Christopher; Rowley, Peter (2021). "Rank one isolated p-minimal subgroups in finite groups". Journal of Algebra. 566: 1–93. doi:10.1016/j.jalgebra.2020.08.017.
References
- ↑ 1.0 1.1 "Ulrich Meierfrankenfeld". College of Natural Science, Michigan State University.
- ↑ "Ulrich Meierfrankenfeld". Mathematics Genealogy Project. North Dakota State University.
- ↑ Griess, Robert L. Jr.; Meierfrankenfeld, Ulrich; Segev, Yoav (1989). "A uniqueness proof for the Monster". Annals of Mathematics. Second Series. 130 (3): 567–602. doi:10.2307/1971455. JSTOR 1971455. MR 1025167.
- ↑ Ivanov, A. A. (1999). Geometry of Sporadic Groups I: Petersen and Tilde Geometries. Encyclopedia of Mathematics and its Applications. 76. Cambridge University Press. ISBN 0-521-41362-1. Search this book on
- ↑ Aschbacher, Michael (2004). "The status of the classification of the finite simple groups" (PDF). Notices of the American Mathematical Society. 51 (7): 736–740.
- ↑ Zaldivar, Felipe. "Review: The Finite Simple Groups". Mathematical Association of America.
- ↑ Meierfrankenfeld, Ulrich; Stellmacher, Bernd; Stroth, Gernot (2003). "Finite groups of local characteristic p: an overview". Groups, Combinatorics and Geometry (Durham, 2001). World Scientific. pp. 155–192. MR 1994966. Search this book on
- ↑ Meierfrankenfeld, Ulrich; Shpectorov, Sergey (2023). "Maximal 2-local subgroups of the Monster and Baby Monster". In Ivanov, Alexander A. Algebraic Combinatorics and the Monster Group. London Mathematical Society Lecture Note Series. Cambridge University Press. Search this book on
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