Groups admitting nilpotent fixed-point-free automorphism groups
نویسندگان
چکیده
منابع مشابه
Finite Fixed Point Free Automorphism Groups
Preface A famous theorem by Frobenius in 1901 proves that if a group G contains a proper non trivial subgroup H such that H ∩ g −1 Hg = {1 G } for all g ∈ G \ H, then there exists a normal subgroup N such that G is the semidirect product of N and H. Groups with this property-the so called Frobenius groups-arise in a natural way as transitive permutation groups, but they can also be characterize...
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Here h(G), the Fitting height (also called the nilpotent length) of G, is as defined in [7]. P(G), the 7t-length of G, is defined in an obvious analogy to the definition of ^-length in [2]. Higman [3] proved Theorem 1 in the case w = l (subsequently, without making any assumptions on the solvability of G, Thompson [6] obtained the same result). Hoffman [4] and Shult [5] proved Theorem 1 provide...
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Baumslag conjectured in the 1970s that the automorphism tower of a finitely generated free group (free nilpotent group) must be very short. Dyer and Formanek [9] justified the conjecture concerning finitely generated free groups in the “sharpest sense” by proving that the automorphism group Aut(Fn) of a non-abelian free group Fn of finite rank n is complete. Recall that a group G is said to be ...
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In this article we will find necessary and sufficient conditions for a fixed point free automorphism (fpf automorphism) of a group to be a commuting automorphism. For a given prime we find the smallest order of a non abelian p-group admitting a commuting f...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1980
ISSN: 0021-8693
DOI: 10.1016/0021-8693(80)90135-0