Glasnik Matematicki, Vol. 54, No. 1 (2019), 77-132.

FURTHER RESEARCH PROBLEMS AND THEOREMS ON PRIME POWER GROUPS

Yakov Berkovich and Zvonimir Janko

Department of Mathematics, University of Haifa, Haifa, Israel
e-mail: berkov@math.haifa.ac.il

Department of Mathematics, University of Heidelberg, Heidelberg, Germany
e-mail: janko@mathi.uni-heidelberg.de

Abstract.   Below we state a great number of research problems concerning finite p-groups. This list is a continuation of the six lists in [1, 2, 3, 4, 5, 6]. Below we also stated some new theorems with proofs. For explanation of notation see the beginning of the above volumes.

2010 Mathematics Subject Classification.   20D15

Key words and phrases.   p-groups of exponent p, metacyclic p-groups, metahamiltonian p-groups, self-centralizing subgroups, Hp-subgroups, maximal abelian subgroups, minimal nonabelian subgroups, regular p-groups

Full text (PDF) (free access)

https://doi.org/10.3336/gm.54.1.06

References:

  1. Y. Berkovich, Groups of prime power order, Vol. 1, Walter de Gruyter, Berlin, 2008.
    MathSciNet     CrossRef

  2. Y. Berkovich and Z. Janko, Groups of prime power order, Vol. 2, Walter de Gruyter, Berlin, 2008.
    MathSciNet    

  3. Y. Berkovich and Z. Janko, Groups of prime power order, Vol. 3, Walter de Gruyter, Berlin, 2011.
    MathSciNet     CrossRef

  4. Y. Berkovich and Z. Janko, Groups of prime power order, Vol. 4, Walter de Gruyter, Berlin, 2016.
    MathSciNet     CrossRef

  5. Y. Berkovich and Z. Janko, Groups of prime power order, Vol. 5, Walter de Gruyter, Berlin, 2016.
    MathSciNet     CrossRef

  6. Y. Berkovich and Z. Janko, Groups of prime power order, Vol. 6, Walter de Gruyter, Berlin, 2018.
    MathSciNet    

  7. J. Cossey, Special maximal subgroups of p-groups, Bull. Aust. Math. Soc. 89 (2014), 415-419.
    MathSciNet     CrossRef

  8. M.W. Horosevskii, The automorphism groups of finite p-groups, Algebra i Logika 10 (1971), 81-86 (in Russian).
    MathSciNet    

  9. M.W. Horosevskii, Automorphisms of finite groups, Mat. Sb. (N.S.) 93 (1974), 576-587 (in Russian).
    MathSciNet    
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