Remarks on O. Grün's paper “Beiträge zur Gruppentheorie. III.”
✍ Scribed by Noboru Itǒ
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 477 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Introducing in 1935 the notion of p-normality in the structure theory of finite groups and developing the excellent theory for p-normal and general finite groups1), 0. GaiiN formulated recently the notion of p-regularity, which is a far-reaching generalization of p-normality, a\nd that of p-hprregularity, which is hereditary to normal subgroups and factor groups and is a specialization ot p.regularity2).
Then, it remained open to ask whether any group is p-regular or not and furthermore whether any p-regular group is p-hyperregular or not?). The purpose of this note is to settle them. Now these notiqns are related vaguely to the solubility of the group. It seems to me that this is notable. For example, the weak closure of the centre of a p-Sylow subgroup in itself is always abelian in the general soluble group.