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https://doi.org/10.3336/gm.47.2.08

Finite p-groups all of whose maximal subgroups, except one, have its derived subgroup of order ≤ p

Zvonimir Janko ; Mathematical Institute, University of Heidelberg , 69120 Heidelberg, Germany

Puni tekst: engleski, pdf (113 KB) str. 325-332 preuzimanja: 273* citiraj
APA 6th Edition
Janko, Z. (2012). Finite p-groups all of whose maximal subgroups, except one, have its derived subgroup of order ≤ p. Glasnik matematički, 47 (2), 325-332. https://doi.org/10.3336/gm.47.2.08
MLA 8th Edition
Janko, Zvonimir. "Finite p-groups all of whose maximal subgroups, except one, have its derived subgroup of order ≤ p." Glasnik matematički, vol. 47, br. 2, 2012, str. 325-332. https://doi.org/10.3336/gm.47.2.08. Citirano 09.12.2021.
Chicago 17th Edition
Janko, Zvonimir. "Finite p-groups all of whose maximal subgroups, except one, have its derived subgroup of order ≤ p." Glasnik matematički 47, br. 2 (2012): 325-332. https://doi.org/10.3336/gm.47.2.08
Harvard
Janko, Z. (2012). 'Finite p-groups all of whose maximal subgroups, except one, have its derived subgroup of order ≤ p', Glasnik matematički, 47(2), str. 325-332. https://doi.org/10.3336/gm.47.2.08
Vancouver
Janko Z. Finite p-groups all of whose maximal subgroups, except one, have its derived subgroup of order ≤ p. Glasnik matematički [Internet]. 2012 [pristupljeno 09.12.2021.];47(2):325-332. https://doi.org/10.3336/gm.47.2.08
IEEE
Z. Janko, "Finite p-groups all of whose maximal subgroups, except one, have its derived subgroup of order ≤ p", Glasnik matematički, vol.47, br. 2, str. 325-332, 2012. [Online]. https://doi.org/10.3336/gm.47.2.08

Sažetak
Let G be a finite p-group which has exactly one maximal subgroup H such that |H'|>p. Then we have d(G)=2, p=2, H' is a four-group, G' is abelian of order 8 and type (4,2), G is of class 3 and the structure of G is completely determined. This solves the problem Nr. 1800 stated by Y. Berkovich in [3].

Ključne riječi
Finite p-groups; minimal nonabelian p-groups; commutator subgroups; nilpotence class of p-groups; Frattini subgroups; generators and relations

Hrčak ID: 93947

URI
https://hrcak.srce.hr/93947

Posjeta: 464 *