## dedicated to john cossey on the occasion of his 60th birthday An extension of the well-known Frobenius criterion of p-nilpotence in groups with modular Sylow p-subgroups is proved in the paper. This result is useful to get information about the classes of groups in which every subnormal subgrou
On Subnormal Subgroups of Factorized Groups
โ Scribed by Silvana Franciosi; Francesco de Giovanni; Yaroslav P. Sysak
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 192 KB
- Volume
- 198
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
A finite group G is said to be a PST -group if every subnormal subgroup of G permutes with every Sylow subgroup of G. We shall discuss the normal structure of soluble PST -groups, mainly defining a local version of this concept. A deep study of the local structure turns out to be crucial for obtaini
formation of all nilpotent groups, the F F-subnormal subgroups of G are exactly the subnormal subgroups of G. Let F F be a subgroup-closed saturated formation containing N N. It is rather easy to see that if F F is closed under the product of normal subgroups, then G F F s A F F B F F for every pai
## Introduction. 1. p-groups with Small Groups of Operators. 2. The Number of Solutions to x p s 1 in a Sylow p-subgroup of the Symmetric Group. 3. p-groups with Maximal Elementary Subgroup of Order p 2 . 4. On the Maximal Order of Subgroups of Given Exponent in a p-group. ## 5. p-groups with
We generalize and present simplified proofs almost all elementary lemmas from Section 8 of the Odd Order Paper. In many places we use Hall's enumeration principle and other simple combinatorial arguments. A number of related results are proved as well. Some open questions are posed. แฎ 1998 Academic