Almost fixed-point-free automorphisms of prime order

作者：Wehrfritz Bertram A F^*

来源：Central European Journal of Mathematics, 2011, 9(3): 616-626.

DOI：10.2478/s11533-011-0017-z

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

Let I center dot be an automorphism of prime order p of the group G with C (G) (I center dot) 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.

• 出版日期2011-6