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Original scientific paper
https://doi.org/10.3336/gm.51.2.05

CZ-groups

Kristijan Tabak   ORCID icon orcid.org/0000-0002-7030-4945 ; Rochester Institute of Technology, Zagreb Campus, D.T. Gavrana 15, 10000 Zagreb , Croatia
Mario Osvin Pavčević ; Department of applied mathematics, Faculty of Electrical Engineering and Computing , University of Zagreb , 10 000 Zagreb, Croatia

Fulltext: english, pdf (154 KB) pages 345-358 downloads: 168* cite
APA 6th Edition
Tabak, K. & Pavčević, M.O. (2016). CZ-groups. Glasnik matematički, 51 (2), 345-358. https://doi.org/10.3336/gm.51.2.05
MLA 8th Edition
Tabak, Kristijan and Mario Osvin Pavčević. "CZ-groups." Glasnik matematički, vol. 51, no. 2, 2016, pp. 345-358. https://doi.org/10.3336/gm.51.2.05. Accessed 5 Dec. 2021.
Chicago 17th Edition
Tabak, Kristijan and Mario Osvin Pavčević. "CZ-groups." Glasnik matematički 51, no. 2 (2016): 345-358. https://doi.org/10.3336/gm.51.2.05
Harvard
Tabak, K., and Pavčević, M.O. (2016). 'CZ-groups', Glasnik matematički, 51(2), pp. 345-358. https://doi.org/10.3336/gm.51.2.05
Vancouver
Tabak K, Pavčević MO. CZ-groups. Glasnik matematički [Internet]. 2016 [cited 2021 December 05];51(2):345-358. https://doi.org/10.3336/gm.51.2.05
IEEE
K. Tabak and M.O. Pavčević, "CZ-groups", Glasnik matematički, vol.51, no. 2, pp. 345-358, 2016. [Online]. https://doi.org/10.3336/gm.51.2.05

Abstracts
We describe some aspects of the structure of nonabelian p-groups G for which every nonabelian subgroup has a trivial centralizer in G, i.e. only it's center. We call such groups CZ-groups. The problem of describing the structure of all CZ-groups was posted as one of the first research problems in the open problems list in Yakov Berkovich's book 'Groups of prime power order' Vol 1 ([1]). Among other features of such groups, we prove that a minimal CZ-group must contain at least p5 elements. The structure of maximal abelian subgroups of these groups is described as well.

Keywords
p-group, center; centralizer; Frattini subgroup; minimal nonabelian subgroup

Hrčak ID: 170041

URI
https://hrcak.srce.hr/170041

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