An $ \mathfrak{X} $-crown of a finite soluble group |
| |
| Authors: | S F Kamornikov L A Shemetkov |
| |
| Institution: | 1.Gomel Branch of the International Institute of Labor and Social Relations,Gomel,Belarus;2.F. Skorina Gomel State University,Gomel,Belarus |
| |
| Abstract: | Let G be a finite soluble group and
F\mathfrakX(G) {\Phi_\mathfrak{X}}(G) an intersection of all those maximal subgroups M of G for which
G | / |
\textCor\texteG(M) ? \mathfrakX {{G} \left/ {{{\text{Cor}}{{\text{e}}_G}(M)}} \right.} \in \mathfrak{X} . We look at properties of a section
F( G | / |
F\mathfrakX(G) ) F\left( {{{G} \left/ {{{\Phi_\mathfrak{X}}(G)}} \right.}} \right) , which is definable for any class
\mathfrakX \mathfrak{X} of primitive groups and is called an
\mathfrakX \mathfrak{X} -crown of a group G. Of particular importance is the case where all groups in
\mathfrakX \mathfrak{X} have equal socle length. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
