A note on groups of p-length 1∗
✍ Scribed by I.M Isaacs; Stephen D Smith
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 254 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
A formation is a class 3 of groups which is closed under homomorphic images and is such that each group G has a unique smallest normal subgroup H with factor group in 5. This uniquely determined normal subgroup of G is called the 8-residual subgroup of G and will be denoted here by G,. The formatio
In this note we prove two results concerned with the derived length of p-groups. First, we improve a little a lower bound of P. Hall for the order of a group of a given derived length. Next, we improve a bound for the derived length of a product of two p-groups.
Two celebrated applications of the character theory of finite groups are Burnside's p ␣ q  -Theorem and the theorem of Frobenius on the groups that bear his name. The elegant proofs of these theorems were obtained at the beginning of this century. It was then a challenge to find character-free proo