Almost fixed-point-free automorphisms of prime order

• Autorzy: Bertram Wehrfritz
• Języki publikacji: EN

Abstrakty

EN

Let ϕ be an automorphism of prime order p of the group G with C G(ϕ) finite of order n. We prove the following. If G is soluble of finite rank, then G has a nilpotent characteristic subgroup of finite index and class bounded in terms of p only. If G is a group with finite Hirsch number h, then G has a soluble characteristic subgroup of finite index in G with derived length bounded in terms of p and n only and a soluble characteristic subgroup of finite index in G whose index and derived length are bounded in terms of p, n and h only. Here a group has finite Hirsch number if it is poly (cyclic or locally finite). This is a stronger notion than that used in [Wehrfritz B.A.F., Almost fixed-point-free automorphisms of order 2, Rend. Circ. Mat. Palermo (in press)], where the case p = 2 is discussed.

Słowa kluczowe

EN

Soluble group; Groups of finite Hirsch number; Groups of finite rank; Fixed points of automorphisms of prime order

Kategorie tematyczne

• 20F50: Periodic groups; locally finite groups
• 20F16: Solvable groups, supersolvable groups
• 20E36: Automorphisms of infinite groups [For automorphisms of finite groups, see ]

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 3
• Strony: 616-626

Daty

wydano

2011-06-01

online

2011-03-22

Twórcy

autor

Bertram Wehrfritz

• Queen Mary University of London

Bibliografia

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• [13] Wehrfritz B.A.F., Almost fixed-point-free automorphisms of soluble groups, J. Pure Appl. Algebra, 2011, 215(5), 1112–1115 http://dx.doi.org/10.1016/j.jpaa.2010.07.017
• [14] Wehrfritz B.A.F., Almost fixed-point-free automorphisms of order 2, Rend. Circ. Mat. Palermo (in press)

Identyfikatory

DOI

10.2478/s11533-011-0017-z