Monomial representations of familiar finite groups over finite fields are used to ลฝ . construct infinite semi-direct products of free products of cyclic groups by groups of monomial automorphisms. Finite homomorphic images of these progenitors in which the actions on the group of automorphisms and o
A Construction of the Held Simple Group
โ Scribed by G. Stroth
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 274 KB
- Volume
- 234
- Category
- Article
- ISSN
- 0021-8693
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๐ SIMILAR VOLUMES
## dedicated to helmut wielandt on the occasion of his 90th birthday Let H be a finite group having center Z H of even order. By the classical Brauer-Fowler theorem there can be only finitely many non-isomorphic simple groups G which contain a 2-central involution t for which C G t โผ = H. In this
In this paper, we obtain a quantitative characterization of all finite simple groups. Let ฯ t G denote the set of indices of maximal subgroups of group G and let P G be the smallest number in ฯ t G . We have the following theorems. Theorem 2. Let N and G be finite simple groups. If N divides G , P
We give a new constructive computer-free existence proof of the third group of ลฝ . Janko, J , using the 9-dimensional unitary representation of 3 J over GF 4 . 3 3 Thereby we embed the C .c-geometries for 3 J and J into the 9-dimensional 2 3 3 unitary space and the 9-dimensional projective space, re