Search results for "Sylow-permutable subgroup"

showing 2 items of 2 documents

On finite minimal non-nilpotent groups

2005

[EN] A critical group for a class of groups X is a minimal non-X-group. The critical groups are determined for various classes of finite groups. As a consequence, a classification of the minimal non-nilpotent groups (also called Schmidt groups) is given, together with a complete proof of Gol¿fand¿s theorem on maximal Schmidt groups.

Pure mathematicsFinite groupPst-groupMathematical societyApplied MathematicsGeneral MathematicsGrups Teoria deSchmidt groupSylow subgroupSylow-permutable subgroupAlgebraMinimal non-nilpotent groupNilpotentCritical groupÀlgebraAlgebra over a fieldFinite groupClass of finite groupsMATEMATICA APLICADACritical groupVolume (compression)Mathematics
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A note on finite PST-groups

2007

[EN] A finite group G is said to be a PST-group if, for subgroups H and K of G with H Sylow-permutable in K and K Sylow-permutable in G, it is always the case that H is Sylow-permutable in G. A group G is a T*-group if, for subgroups H and K of G with H normal in K and K normal in G, it is always the case that H is Sylow-permutable in G. In this paper, we show that finite PST-groups and finite T*-groups are one and the same. A new characterisation of soluble PST-groups is also presented.

Transitive normalityGrups Teoria deÀlgebraFinite groupMATEMATICA APLICADASylow-permutable subgroup
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