×

“Hasse principle” for extraspecial \(p\)-groups. (English) Zbl 0995.20034

Authors’ summary: A group \(G\) is said to enjoy the “Hasse principle” if every local coboundary of \(G\) is a global coboundary. It is proved that every non-Abelian finite \(p\)-group having a maximal subgroup which is cyclic and every extraspecial \(p\)-group enjoy the “Hasse principle”.

MSC:

20J05 Homological methods in group theory
20D15 Finite nilpotent groups, \(p\)-groups
Full Text: DOI

References:

[1] Gaschütz, W.: Kohomogische Trivialitäten und äussere Automorphismen von \(p\)-gruppen. Math. Z., 88 , 432-433 (1965). · Zbl 0199.06302 · doi:10.1007/BF01112225
[2] Gaschütz, W.: Nichtabelsche \(p\)-Gruppen besitzen äussere \(p\)-Automorphismen. J. Algebra, 4 , 1-2 (1966). · Zbl 0142.26001 · doi:10.1016/0021-8693(66)90045-7
[3] Ono, T.: “Shafarevich-Tate sets” for profinite groups. Proc. Japan Acad., 75A , 96-97 (1999). · Zbl 0997.20036 · doi:10.3792/pjaa.75.96
[4] Ono, T., and Wada, H.: “Hasse principle” for free groups. Proc. Japan Acad., 75A , 1-2 (1999). · Zbl 0928.20022 · doi:10.3792/pjaa.75.1
[5] Ono, T., and Wada, H.: “Hasse principle” for symmetric and alternating groups. Proc. Japan Acad., 75A , 61-62 (1999). · Zbl 0948.20001 · doi:10.3792/pjaa.75.61
[6] Suzuki, M.: Group Theory I. Springer, New York-Berlin-Heidelberg-Tokyo (1982). · Zbl 0472.20001
[7] Suzuki, M.: Group Theory II. Springer, New York-Berlin-Heidelberg-Tokyo (1986). · Zbl 0586.20001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.