Glasnik matematički, Vol. 47 No. 2, 2012.
Izvorni znanstveni članak
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
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
Datum izdavanja:
19.12.2012.
Posjeta: 834 *