Fitting height of solvable groups admitting an automorphism of prime order with abelian fixed-point subgroup
نویسندگان
چکیده
منابع مشابه
Solvable Groups Admitting a Fixed-point-free Automorphism of Prime Power Order
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...
متن کاملFinite Groups Admitting a Fixed-Point-Free Automorphism of Order 4
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive o...
متن کاملA Generalized Fixed Point Free Automorphism of Prime Power Order
Let G be a finite group and α be an automorphism of G of order p n for an odd prime p. Suppose that α acts fixed point freely on every α-invariant p-section of G, and acts trivially or exceptionally on every elementary abelian α-invariant p-section of G. It is proved that G is a solvable p-nilpotent group of nilpotent length at most n + 1, and this bound is best possible.
متن کاملFinite Groups with Fixed-point-free Automorphisms of Prime Order.
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive o...
متن کاملAsymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power order
We show that almost every Cayley graph Γ of an abelian group G of odd prime-power order has automorphism group as small as possible. Additionally, we show that almost every Cayley (di)graph Γ of an abelian group G of odd prime-power order that does not have automorphism group as small as possible is a normal Cayley (di)graph of G (that is, GL/Aut(Γ)).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1981
ISSN: 0021-8693
DOI: 10.1016/0021-8693(81)90287-8