On 2-groups with no normal abelian subgroups of rank 3, and their occurrence as Sylow 2-subgroups of finite simple groups
Open Access
- 1 January 1970
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 150 (2) , 345-408
- https://doi.org/10.1090/s0002-9947-1970-0276324-3
Abstract
We prove that in a finite 2 2 -group with no normal Abelian subgroup of rank ≧ 3 \geqq 3 , every subgroup can be generated by four elements. This result is then used to determine which 2 2 -groups T T with no normal Abelian subgroup of rank ≧ 3 \geqq 3 can occur as S 2 {S_2} ’s of finite simple groups G G , under certain assumptions on the embedding of T T in G G .Keywords
This publication has 8 references indexed in Scilit:
- Endliche Gruppen IPublished by Springer Nature ,1967
- Central elements in core-free groupsJournal of Algebra, 1966
- Some applications of the theory of blocks of characters of finite groups. IIJournal of Algebra, 1964
- Centralizers of abelian normal subgroups of p-groupsJournal of Algebra, 1964
- Bibliography, from Solvability of groups of odd order, Pacific J. Math., vol. 13, no. 3 (1963Pacific Journal of Mathematics, 1963
- Suzuki $2$-groupsIllinois Journal of Mathematics, 1963
- Generalizations of Certain Elementary Theorems on p -GroupsProceedings of the London Mathematical Society, 1961
- On a special class of p-groupsActa Mathematica, 1958