Topic
Z-group
About: Z-group is a research topic. Over the lifetime, 339 publications have been published within this topic receiving 11263 citations.
Papers published on a yearly basis
Papers
More filters
Book•
[...]
01 Jan 1959
TL;DR: The theory of normal subgroups and homomorphisms was introduced in this article, along with the theory of $p$-groups regular $p-groups and their relation to abelian groups.
Abstract: Introduction Normal subgroups and homomorphisms Elementary theory of abelian groups Sylow theorems Permutation groups Automorphisms Free groups Lattices and composition series A theorem of Frobenius solvable groups Supersolvable and nilpotent groups Basic commutators The theory of $p$-groups regular $p$-groups Further theory of abelian groups Monomial representations and the transfer Group extensions and cohomology of groups Group representation Free and amalgamated products The Burnside problem Lattices of subgroups Group theory and projective planes Bibliography Index Index of special symbols.
2,960 citations
TL;DR: In this article, a class of doubly transitive groups satisfying the condition that the identity is the only element leaving three distinct letters fixed was investigated. But the main object of the investigation was to classify the groups which do not contain a regular normal subgroup of order 1 + N in case N is even.
Abstract: : This study considers a class of doubly transitive groups satisfying the condition that the identity is the only element leaving three distinct letters fixed. The main object of the investigation is to classify the groups which do not contain a regular normal subgroup of order 1 + N in case N is even. (Author)
743 citations
TL;DR: In this article, the atlas covers groups from the families of the classification of finite simple groups, and includes a classification of simple groups with respect to finite simple classes of groups.
Abstract: This atlas covers groups from the families of the classification of finite simple groups. Recently updated incorporating corrections
662 citations
Book•
17 Apr 2010
TL;DR: The alternating groups are the classical groups, the exceptional groups, and the sporadic groups as mentioned in this paper, which are the groups with the highest correlation between the classical group and the exceptional group.
Abstract: The alternating groups.- The classical groups.- The exceptional groups.- The sporadic groups.
428 citations
Book•
28 Oct 1999
TL;DR: Pro-p groups of finite co-class were studied in this paper, where the authors showed that the poincare series can be used to define analytic groups over pro-p rings.
Abstract: Prelude Part I. Pro-p Groups: 1. Profinite groups and pro-p groups 2. Powerful p-groups 3. Pro-p groups of finite rank 4. Uniformly powerful groups 5. Automorphism groups Interlude A. Fascicule de resultats: pro-p groups of finite rank Part II. Analytic Groups: 6. Normed algebras 7. The group algebra Interlude B. Linearity criteria 8. P-adic analytic groups Interlude C. Finitely generated groups, p-adic analytic groups and Poincare series 9. Lie theory Part III. Further Topics: 10. Pro-p groups of finite co-class 11. Dimension subgroup methods 12. Some graded algebras Interlude D. The Golod Shafarevic inequality Interlude E. Groups of sub-exponential growth 13. Analytic groups over pro-p rings.
421 citations