6533b856fe1ef96bd12b31a0
RESEARCH PRODUCT
Finite groups with all minimal subgroups solitary
Orieta LirianoRamon Esteban-romerosubject
p-groupNormal subgroupFinite groupAlgebra and Number TheoryApplied MathematicsAstrophysics::Instrumentation and Methods for AstrophysicsMinimal subgroupGrups Teoria deComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Fitting subgroupCombinatoricsMathematics::Group TheoryLocally finite groupExtra special groupComputer Science::General LiteratureOmega and agemo subgroupSolitary subgroupÀlgebraIndex of a subgroupFinite groupMATEMATICA APLICADAMathematicsdescription
We give a complete classification of the finite groups with a unique subgroup of order p for each prime p dividing its order. All the groups considered in this paper will be finite. One of the most fruitful lines in the research in abstract group theory during the last years has been the study of groups in which the members of a certain family of subgroups satisfy a certain subgroup embedding property. The family of the subgroups of prime order (also called minimal subgroups) has attracted the interest of many mathematicians. For example, a well-known result of Itˆo (see [8, Kapitel III, Satz 5.3; 9]) states that a group of odd order with all minimal subgroups in the center is nilpotent. The following result of Gasch¨utz and Itˆo (see [5, Kapitel IV, Satz 5.7; 9]) gives interesting properties of groups with all minimal subgroups normal.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-01-01 |