Geodesic
Finite groups with seminormal Schmidt subgroups
Algebra i logika, Tome 46 (2007) no. 4, pp. 448-458

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A non-nilpotent finite group whose proper subgroups are all nilpotent is called a Schmidt group. A subgroup $A$ is said to be seminormal in a group $G$ if there exists a subgroup $B$ such that $G=AB$ and $AB_1$ is a proper subgroup of $G$, for every proper subgroup $B_1$ of $B$. Groups that contain seminormal Schmidt subgroups of even order are considered. In particular, we prove that a finite group is solvable if all Schmidt $\{2,3\}$-subgroups and all 5-closed $\{2,5\}$-Schmidt subgroups of the group are seminormal; the classification of finite groups is not used in so doing. Examples of groups are furnished which show that no one of the requirements imposed on the groups is unnecessary.
Keywords: finite group, Schmidt subgroup, subnormal subgroup, seminormal subgroup.
Mots-clés : solvable group 
@article{AL_2007_46_4_a2,
     author = {V. N. Knyagina and V. S. Monakhov},
     title = {Finite groups with seminormal {Schmidt} subgroups},
     journal = {Algebra i logika},
     pages = {448--458},
     publisher = {mathdoc},
     volume = {46},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_4_a2/}
}
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V. N. Knyagina; V. S. Monakhov. Finite groups with seminormal Schmidt subgroups. Algebra i logika, Tome 46 (2007) no. 4, pp. 448-458. http://geodesic.mathdoc.fr/item/AL_2007_46_4_a2/