Naslov
On subgroups of finite p-groups

Autori
Berkovich, Yakov ; Janko, Zvonimir

Izvornik
Israel journal of mathematics (0021-2172) 171 (2009); 29-49

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
metacyclic p-groups; p-groups of maximal class; minimal nonabelian p-groups; regular p-groups

Sažetak
In 2 we prove that if a 2-group G and all its nonabelian maximal subgroups are two-generator, then G is either metacyclic or minimal nonabelian. In 3 we consider similar question for p > 2. In 4 the 2-groups all of whose minimal nonabelian subgroups have order 16 and a cyclic subgroup of index 2, are classified. It is proved, in 5 that if G is a nonmetacyclic two-generator 2-group and A, B, C are all its maximal subgroups with d(A) <= d(B) <= d(C), then d(C) = 3 and either d(A) = d(B) = 3 (this occurs if and only if G/G' has no cyclic subgroup of index 2) or else d(A) = d(B) = 2. Some information on the last case is obtained in Theorem 5.3.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena
Janko, Zvonimir je suradnik na projektu iz dijaspore, UNI Heidelberg, Deutschland.

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