Finite groups admitting a fixed-point-free automorphism
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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متن کاملFixed point free automorphisms of groups related to finite fields
Let G = Fqo 〈β〉 be the semidirect product of the additive group of the field of q = p elements and the cyclic group of order d generated by the invertible linear transformation β defined by multiplication by a power of a primitive root of Fq. We study endomorphisms of G. We find an arithmetic condition on d so that every endomorphism is determined by its values on (1, 1) and (0, β). When that i...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1968
ISSN: 0021-8693
DOI: 10.1016/0021-8693(68)90089-6