Some $p$-groups of maximal class
نویسندگان
چکیده
منابع مشابه
Automorphisms of P-groups of Maximal Class
Juhász has proved that the automorphism group of a group G of maximal class of order p, with p ≥ 5 and n > p + 1, has order divisible by p. We show that by translating the problem in terms of derivations, the result can be deduced from the case where G is metabelian. Here one can use a general result of Caranti and Scoppola concerning automorphisms of two-generator, nilpotent metabelian groups.
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Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...
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1. A group of prime-power order p is obviously nilpotent of class at most m — 1; if it has class precisely m — 1, it is said to be of maximal class. The derived length of a p-group of maximal class is bounded by log2(3p-3) if p is odd and by 2 if p = 2. Indeed, if m ^ 9 p 4 0 , the derived length is at most 3 (Shepherd [6], Leedham-Green and McKay [5].) The question of whether there is an uncon...
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let g be a group. a subset x of g is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in x. if |x| ≥ |y | for any other set of pairwise non-commuting elements y in g, then x is said to be a maximal subset of pairwise non-commuting elements. in this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1974
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1974-0349835-3