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On certain subgroups of a minimal simple finite group of odd order
In mathematical
finite group theory, Thompson's original uniqueness theorem (
Feit & Thompson 1963, theorems 24.5 and 25.2) states that in a minimal
simple finite
group of odd
order there is a unique maximal
subgroup containing a given
elementary abelian subgroup of
rank 3.
Bender (1970) gave a shorter proof of the uniqueness theorem.
References
- Bender, Helmut (1970),
"On the uniqueness theorem", Illinois Journal of Mathematics, 14 (3): 376–384,
doi:
10.1215/ijm/1256053074,
ISSN
0019-2082,
MR
0262351
- Bender, Helmut;
Glauberman, George (1994), Local analysis for the odd order theorem, London Mathematical Society Lecture Note Series, vol. 188,
Cambridge University Press,
ISBN
978-0-521-45716-3,
MR
1311244
-
Feit, Walter;
Thompson, John G. (1963),
"Solvability of groups of odd order", Pacific Journal of Mathematics, 13: 775–1029,
doi:
10.2140/pjm.1963.13.775,
ISSN
0030-8730,
MR
0166261