Glasnik matematički, Vol. 45 No. 1, 2010.
Original scientific paper
https://doi.org/10.3336/gm.45.1.05
Characterization of finite abelian and minimal nonabelian groups
Yakov Berkovich
; Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel
Abstract
In this note we present the following characterizations of finite abelian and minimal nonabelian groups:
(i) A group G is abelian if and only if G' = Φ(G)'.
(ii) A group G is either abelian or minimal nonabelian if and only if Φ(G)' = H' for all maximal subgroups H of G.
We also prove a number of related results.
Keywords
Maximal subgroup; abelian; minimal nonabelian; minimal nonnilpotent and Frobenius groups; Frattini subgroup; derived subgroup
Hrčak ID:
52367
URI
Publication date:
17.5.2010.
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