On non-periodic groups with non-Dedekind norm of Abelian noncyclic subgroups

F.N. Liman (Makarenko Sumy State Pedagogical University)
M.G. Drushliak (Makarenko Sumy State Pedagogical University), https://orcid.org/0000-0002-9648-2248

Abstract


Non-periodic groups without free Abelian subgroups of rank 2 with non-Dedekind norm of Abelian noncyclic subgroups are studied.

Keywords


non-periodic group; normality; normalizer; norm; norm of Abelian noncyclic subgroups

References


Drushliak M.G. "On norm of Abelian noncyclic groups in non-periodic groups", Visnyk Kyiv univ. Fiz.-mat. nauky, 2009; 1: pp. 14-18. (in Ukrainian)

Liman F.N. "Groups with constraints on normalizers of different systems of subgroups", Depon. in DNTB of Ukraine 24.11.97, #577, 97. (in Ukrainian)

Lukashova T.D. "On norm of Abelian noncyclic subgroups of infinite locally finite $$$p$$$-groups", Visnyk Kyiv univ. Fiz.-mat. nauky, 2004; 3: pp. 35-39. (in Ukrainian)

Semko M.M. Groups with conditions of density of normality and its generalizations for some systems, 1998. (in Ukrainian)

Baer R. "Der Kern, eine Charakteristische Untergruppe", Comp. Math., 1934; 1: pp. 254-283. (in German)

Beidleman J.C., Heineken H., Newell M. "Centre and norm", Bull. Austral. Math. Soc., 2004; 69(3): pp. 457-464. doi:10.1017/S0004972700036248

Schenkman E. "On the Norm of a Group", Illinois J. Math., 1960; 4(1): pp. 150-152. doi:10.1215/ijm/1255455741

Wang J., Guo X. "On the norm of finite groups", Algebra Colloquium, 2007; 14: pp. 605-612. doi:10.1142/S1005386707000557

Wos L. "On commutative prime power subgroups of the norm", Illinois J. Math., 1958; 2(2): pp. 271-284. doi:10.1215/ijm/1255381349


Liman F.N. "Non-periodic groups with some systems of normal subgroups", Algebra Logic, 1968; 7(4): pp. 70-86.

Chernikov S.N. Groups with given properties of systems of subgroups, 1980.




DOI: https://doi.org/10.15421/241113

  

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Copyright (c) 2011 F.N. Liman, M.G. Drushliak

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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