Glasnik Matematicki, Vol. 42, No.2 (2007), 319-343.
ALTERNATE PROOFS OF TWO CHARACTERIZATION THEOREMS OF MILLER AND JANKO
ON 2-GROUPS, AND SOME RELATED RESULTS
Yakov Berkovich
Department of Mathematics, University of Haifa, Mount Carmel,
Haifa 31905, Israel
e-mail: berkov@math.haifa.ac.il
Abstract. We study the p-groups all of whose nonabelian
maximal subgroups are decomposable in direct or central product of
two groups with specific structures.
2000 Mathematics Subject Classification.
20D15.
Key words and phrases. Minimal nonabelian p-groups, p-groups of maximal
class, minimal non Dedekindian 2-groups, direct product, central
product.
Full text (PDF) (free access)
DOI: 10.3336/gm.42.2.07
References:
- Y. Berkovich, On subgroups of finite p-groups,
J. Algebra 224 (2000), 198-240.
MathSciNet
CrossRef
- Y. Berkovich, On abelian subgroups of finite p-groups,
J. Algebra 199 (1998), 262-280.
MathSciNet
- Y. Berkovich, On subgroups and epimorphic images of finite
p-groups, J. Algebra 248 (2002), 472-553.
MathSciNet
CrossRef
- Y. Berkovich, Alternate
proofs of some basic theorems of finite group theory,
Glas. Mat. Ser. III 40 (2005), 207-233.
MathSciNet
CrossRef
- Y. Berkovich, Groups of Prime Power Order, Part I, in
preparation.
- Y. Berkovich and Z. Janko, Groups of Prime Power Order, Part
II, in preparation.
- Y. Berkovich and Z. Janko, Structure of finite p-groups with
given subgroups, Cont. Math. 402 (2006), 13-93.
MathSciNet
- Y. Berkovich and Z. Janko, On subgroups of finite p-groups,
Israel J. Math., to appear.
- Ya. G. Berkovich and E. M. Zhmud', Characters of Finite Groups,
Part 1, AMS, Providence, RI, 1998.
MathSciNet
- N. Blackburn, On a special class of p-groups, Acta Math.
100 (1958), 45-92.
MathSciNet
CrossRef
- I. M. Isaacs, Character Theory of Finite Groups, Acad. Press, NY,
1976.
MathSciNet
- Z. Janko, personal communication.
- Z. Janko, On finite nonabelian 2-groups all of whose minimal
nonabelian subgroups are of exponent 4, J. Algebra 315
(2007), 801-808.
MathSciNet
CrossRef
- Z. Janko, Finite 2-groups all of whose nonabelian subgroups
are generated by involutions, Math. Z. 252 (2006), 419-420.
MathSciNet
CrossRef
- G. A. Miller, The groups in which every subgroup is either
abelian or hamiltonian, Trans. Amer. Math. Soc. (1907), 25-29.
MathSciNet
CrossRef
- G. A. Miller, The groups in which every subgroup is either
abelian or dihedral, Amer. Math. J. 29 (1907), 289-294.
MathSciNet
CrossRef
- G. A. Miller, H. F. Blichfeldt and L. E. Dickson, Theory and
Applications of Finite Groups, NY, Stechert, 1938.
- L. Redei, Das "schiefe Produkt" in der Gruppentheorie mit
Anwendung auf die endlichen nichtkommutativen Gruppen mit lauter
kommutativen echten Untergruppen und die Ordnungzahlen, zu denen nur
kommutative Gruppen gehören, Comment. Math. Helvet. 20
(1947), 225-267.
MathSciNet
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