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Theorems on the theory of substitutions. (Théorèmes sur les groupes de substitutions.) () JFM 04.0056.02
Bezeichnet $n^\alpha$ die höchste Potenz der Primzahl $n$, welche die Ordnung von $G$ theilt, so enthält diese Gruppe eine andere von der Ordnung $n^\alpha$. Hieran schliessen sich ähnliche Theoreme über enthaltene Gruppen. Wenn die Ordnung einer algebraischen Gleichung $=n^\alpha n_1^{\alpha_1}n_2^{\alpha_2}\cdots$ ist, wobei $n,n_1,n_2,\cdots$ Primzahlen sind, und $n>n_1^{\alpha_1}n_2^{\alpha_2}\cdots, n_1>n_2^{\alpha_2}\cdots$ ist, so ist die Gleichung durch Wurzeln lösbar. Es folgt eine Untersuchung der wichtigsten Eigenschaften transitiver Gruppen.
Reviewer: Netto, Dr. (Berlin)

20D20Sylow subgroups of finite groups, Sylow properties, $\pi$-groups, $\pi$-structure
20B20Multiply transitive finite permutation groups
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