naa a22 4500 510783392 CHVBK 20180411083254.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s11856-012-0121-1 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0121-1 Berkovich Yakov Department of Mathematics, University of Haifa, 31905, Mount Carmel, Haifa, Israel aut Maximal abelian and minimal nonabelian subgroups of some finite two-generator p -groups especially metacyclic [Elektronische Daten] [Yakov Berkovich] We study the subgroup structure of some two-generator p-groups and apply the obtained results to metacyclic p-groups. For metacyclic p-groups G, p > 2, we do the following: (a) compute the number of nonabelian subgroups with given derived subgroup, show that (ii) minimal nonabelian subgroups have equal order, (c) maximal abelian subgroups have equal order, (d) every maximal abelian subgroup is contained in a minimal nonabelian subgroup and all maximal subgroups of any minimal nonabelian subgroup are maximal abelian in G. We prove the same results for metacyclic 2-groups (e) with abelian subgroup of index p, (f) without epimorphic image ≅ D8. The metacyclic p-groups containing (g) a minimal nonabelian subgroup of order p 4, (h) a maximal abelian subgroup of order p 3 are classified. We also classify the metacyclic p-groups, p > 2, all of whose minimal nonabelian subgroups have equal exponent. It appears that, with few exceptions, a metacyclic p-group has a chief series all of whose members are characteristic. Hebrew University Magnes Press, 2012 Israel Journal of Mathematics Springer US; http://www.springer-ny.com 194/2(2013-03-01), 831-869 0021-2172 194:2<831 2013 194 11856 https://doi.org/10.1007/s11856-012-0121-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0121-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Berkovich Yakov Department of Mathematics, University of Haifa, 31905, Mount Carmel, Haifa, Israel aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 194/2(2013-03-01), 831-869 0021-2172 194:2<831 2013 194 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer