It is proved that if a locally nilpotent group \(G\) admits an almost regular automorphism of prime order \(p\) then \(G\) contains a nilpotent subgroup \(G_{1}\) such that \(\left|G: G_{1}\right| \leqslant f(p, m)\) and the class of nilpotency of \(G_{1} \leqslant g(p)\), where \(f\) is a function
Groups with regular automorphisms of order four
✍ Scribed by L. G. Kovács
- Publisher
- Springer-Verlag
- Year
- 1961
- Tongue
- French
- Weight
- 983 KB
- Volume
- 75
- Category
- Article
- ISSN
- 0025-5874
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📜 SIMILAR VOLUMES
In this paper we prove that there are functions f ( p, m, n) and h(m) such that any finite p-group with an automorphism of order p n , whose centralizer has p m points, has a subgroup of derived length h(m) and index f ( p, m, n). This result gives a positive answer to a problem raised by E. I. Khuk
## Abstract We consider one‐factorizations of __K__~2__n__~ possessing an automorphism group acting regularly (sharply transitively) on vertices. We present some upper bounds on the number of one‐factors which are fixed by the group; further information is obtained when equality holds in these boun