6533b7cffe1ef96bd125852f
RESEARCH PRODUCT
Some results concerning simple locally finite groups of 1-type
Orazio PuglisiFelix Leinensubject
Discrete mathematicsAlgebra and Number TheoryProfinite groupGroup ringsGroup (mathematics)Inductive systemsSimple groupsCovering groups of the alternating and symmetric groupsLocally finite groupsGroup of Lie typeSymmetric groupSimple groupClassification of finite simple groupsGroup theoryMathematicsdescription
AbstractIn this paper several aspects of infinite simple locally finite groups of 1-type are considered. In the first part, the classes of diagonal limits of finite alternating groups, of diagonal limits of finite direct products of alternating groups, and of absolutely simple groups of 1-type are distinguished from each other. In the second part, inductive systems of representations over fields of characteristic zero (which are known to correspond to ideals in the group algebra) are studied in general for groups of 1-type. The roles of primitive respectively imprimitive representations in inductive systems are investigated. Moreover it is shown that in any proper inductive system the depths of the representations of certain alternating subgroups are bounded.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-05-01 | Journal of Algebra |