Finite p-groups all of whose maximal subgroups, except one, have its derived subgroup of order ≤ p
نویسندگان
چکیده
منابع مشابه
FINITE p-GROUPS ALL OF WHOSE MAXIMAL SUBGROUPS, EXCEPT ONE, HAVE ITS DERIVED SUBGROUP OF ORDER ≤ p
Let G be a finite p-group which has exactly one maximal subgroup H such that |H| > p. Then we have d(G) = 2, p = 2, H is a four-group, G is abelian of order 8 and type (4, 2), G is of class 3 and the structure of G is completely determined. This solves the problem Nr. 1800 stated by Y. Berkovich in [3]. We consider here only finite p-groups and our notation is standard (see [1]). If G is a p-gr...
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Introduction. Dedekind has determined all groups whose subgroups are all normal (see, e.g., [5, Theorem 12.5.4]). Partially generalizing this, Wielandt showed that a finite group is nilpotent, if and only if all its subgroups are subnormal, and also if and only if all maximal subgroups are normal [5, Corollary 10.3.1, 10.3.4]. Huppert [7, Sätze 23, 24] has shown that if all 2nd-maximal subgroup...
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ژورنال
عنوان ژورنال: Glasnik matematicki
سال: 2012
ISSN: 0017-095X
DOI: 10.3336/gm.47.2.08