University of Tehran
Journal of Sciences, Islamic Republic of Iran
10161104
9
3
1998
09
01
PERMUTATION GROUPS WITH BOUNDED
MOVEMENT ATTAINING THE BOUNDS FOR
ODD PRIMES

31245
EN
Journal Article
1970
01
01
Let G be a transitive permutation group on a set ? and let m be a positive integer.
If no element of G moves any subset of ? by more than m points, then ?  [2mp I
(p1)] wherep is the least odd primedividing G . When the bound is attained, we show that  ?  = 2 p q ….. q where ? is a nonnegative integer with 2 < p, r 1 and q is a prime satisfying p < q < 2p, ? = 0 or 1, I i n. Furthermore, every 2element of G fixes at least [2m/(p 1)] points and each q element of G fixes at least [2m(q p)/(p 1)( q  l)] points. Finally, we prove that if G is a pgroup of exponent, at least p2 and I ? l = [2mp /(p l)], then every fixed point free element of G has order p.
https://jsciences.ut.ac.ir/article_31245_74cddceca869ec8a5dae4cc763751189.pdf