Corsi Tani, Gabriella:
Su una congettura di J.R. Durbin e M. McDonald
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 69 (1980), fasc. n.3-4, p. 106-110, (Italian)
pdf (356 Kb), djvu (556 Kb). | MR 0670814 | Zbl 0512.20010
Sunto
In this Note it is proved that a finite $p$-grou $G$, which is not abelian of type $(2,2)$, has a c.c.s. (characteristic cyclic series) if and only if $Aut \, G$ is supersoluble. It follows that a supersoluble group can occur as automorphism group of a finite $p$-group (nonabelian of type $(2,2)$) only if strictly $p$-closed.
Referenze Bibliografiche
[1]
R. Baer (
1957) -
Classes of finite groups and their properties.
«Illinois J. Math.»,
I, 115-187. |
Zbl 0077.03003[2]
R. Baer (
1959) -
Supersoluble Immersion.
«Canad. J. Math.»,
II, 353-369. |
Zbl 0088.02402[3]
R. Baer (
1969) -
Principal factors, maximal subgroups, ecc.,
«Illinois J. Math.»,
13, 1-52. |
Zbl 0202.02401[5] G. Corsi Tani (1974) - Gruppi $\Sigma$-solubili $\Sigma$-nilpotenti. «Istituto Matematico Ulisse Dini», I, 1-31.
[6] M. Curzio (1976) - Gruppi risolubili a sottogruppi subnormali caratteristici. «Symposia Math.», 17, 283-300.
[7]
J.R. Durbin,
M. McDonald (
1971) -
Groups with a characteristic cyclic series,
«J. Algebra»,
18, 453-460. |
Zbl 0222.20011[8] D. Gorenstein (1968) - Finite Groups. Harper & Row.
[9]
B. Huppert (
1954) -
Normalteiler und maximale Untergruppen endlicher Gruppen.
«Math. Z.»,
60, 409-434. |
fulltext EuDML |
Zbl 0057.25303[10]
B. Huppert (
1967) -
Endliche Gruppen I.
Springer Verlag. |
Zbl 0217.07201[11]
R. Laue (
1976) -
Zur Charakterisierung der Fittinggruppe der Automorphismengruppe einer endlichen Gruppe.
«J. Algebra»,
40, 618—626. |
Zbl 0343.20009[12] P. Schmid (1972) - Untergruppenreihen normalisierende Automorphismengruppen. «Arch. Math. (Basel)», 23, 459-468.
[13]
P. Schmid (
1976) -
Normal $p$-Subgroups in the Group of outer automorphisms of a finite $p$-group.
«Math. Z.»,
147, 271-277. |
fulltext EuDML |
Zbl 0307.20016[14] S.A. Syskin (1968) - Super-solvable groups of automorphisms of finite solvable groups. «Algebra i Logika», 7, 105-107.