Über minimale k-irreguläre p-Gruppen. I. (On minimally k-irregular p- groups. I)
The author continues his study of k-regular p-groups and in this paper investigates how far the results of Mann on minimally irregular p-groups carry over to the k-regular case. Minimally k-irregular p-groups are those which are not themselves k-regular but in which every proper section is k-regular. Various properties proved in the case \(k=1\) by Mann are examined; it is shown for instance that a minimally k-irregular p- group is generated by two elements, has cyclic centre, is \(p^ k\)- abelian and so on. Examples are then constructed which show that, in contrast to the case \(k=1\), the exponent of the derived subgroup and the type of its factor group are not uniquely determined. Finally, an example is constructed which shows that given integers \(e>k>0\), there exists a minimally k-regular p-group of exponent \(p^ e\).
scientific article; zbMATH DE number 4002362
scientific article