6533b7ddfe1ef96bd127495c
RESEARCH PRODUCT
ON A QUESTION OF BEIDLEMAN AND ROBINSON
Adolfo Ballester-bolinchesRamon Esteban-romerosubject
Pure mathematicsAlgebra and Number TheoryFinite soluble groupGroup (mathematics)Permutizer conditionPrime numberGrups Teoria deAutomorphismCombinatoricsConverseChief factorOrder (group theory)ÀlgebraAlgebra over a fieldMATEMATICA APLICADAMathematicsCounterexampledescription
[EN] In [J. C. Beidleman, D. J. S. Robinson, J. Algebra 1997, 191, 686--703, Theorem A], Beidleman and Robinson proved that if a group satisfies the permutizer condition, it is soluble, its chief factors have order a prime number or 4 and G induces the full group of automorphisms in the chief factors of order 4. In this paper, we show that the converse of this theorem is false by showing some counterexamples. We also find some sufficient conditions for a group satisfying the converse of that theorem to satisfy the permutizer condition.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-01-01 | Communications in Algebra |