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Nilpotent injectors in finite groups
| Content Provider | Scilit |
|---|---|
| Author | Förster, Peter |
| Copyright Year | 1985 |
| Description | Nilpotent injectors exist in all finite groups.For every Fitting class F of finite groups (see [2]), $Inj_{F}$(G) denotes the set of all H ≤ G such that for each N ⊴ ⊴ G , H ∩ N is an F -maximal subgroup of N (that is, belongs to F and i s maximal among the subgroups of N with this property). Let W and N* denote the Fitting class of all nilpotent and quasi-nilpotent groups, respectively. (For the basic properties of quasi-nilpotent groups, and of the N*-radical F*(G) of a finite group G3 the reader is referred to [5].,X. %13; we shall use these properties without further reference.) Blessenohl and H. Laue have shown in CJ] that for every finite group G, $Inj_{N*}$(G) = {H ≤ G | H ≥ F*(G) N*-maximal in G} is a non-empty conjugacy class of subgroups of G. More recently, Iranzo and Perez-Monasor have verified $Inj_{N}$(G) ≠ Φ for all finite groups G satisfying G = $C_{G}$(E(G))E(G) (see [6]), and have extended this result to a somewhat larger class M of finite groups C(see [7]). One checks, however, that M does not contain all finite groups; for example, $S_{5}$ ε M. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2CEB1209BD00BD8A70D04867BBEA47D8/S0004972700009965a.pdf/div-class-title-nilpotent-injectors-in-finite-groups-div.pdf |
| Ending Page | 297 |
| Page Count | 5 |
| Starting Page | 293 |
| ISSN | 00049727 |
| e-ISSN | 17551633 |
| DOI | 10.1017/s0004972700009965 |
| Journal | Bulletin of the Australian Mathematical Society |
| Issue Number | 2 |
| Volume Number | 32 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1985-10-01 |
| Access Restriction | Open |
| Subject Keyword | Bulletin of the Australian Mathematical Society Nilpotent Groups Finite Groups |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
