ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 20 Makarenko, Natalia, Institute of Mathematics, Novosibirsk, Russia: Finite 2-groups with automorphisms of order four. Kovacs’s theorem [1] states that the second term of the derived series of a locally finite or locally nilpotent group G with an automorphism of order 4 without non-trivial fixed elements lies in the centre of G. It is proved that a finite 2-group G admitting an automorphism of order 4 with exactly m fixed points contains a subgroup H of m-bounded index in G such that the second term of the derived series of H lies in the centre of H. Earlier in [2] it was proved that under the same conditions G contains a subgroup of m-bounded index, whose commutator subgroup is nilpotent of class at most 3. Reference: 1. L. G. Kovács, Groups with regular automorphisms of order four, Math. Z. , 75 (1961), 277-294. 2. N. Yu. Makarenko, Finite 2-groups admitting an automorphism of order 4 with few fixed points, Algebra and Logic, 32 (1993), 215-230.