FIXED-POINT-FREE PERMUTATIONS IN TRANSITIVE PERMUTATION GROUPS OF PRIME-POWER ORDER

1985 ◽  
Vol 36 (3) ◽  
pp. 273-278 ◽  
Author(s):  
PETER J. CAMERON ◽  
L. G. KOVáCS ◽  
M. F. NEWMAN ◽  
CHERYL E. PRAEGER
Keyword(s):  
Fixed Point ◽  
Prime Power ◽  
Permutation Groups ◽  
Prime Power Order

On permutation groups of prime power order

1980 ◽  
Vol 173 (3) ◽  
pp. 211-215 ◽  
Author(s):  
Christian Ronse
Keyword(s):  
Prime Power ◽  
Permutation Groups ◽  
Prime Power Order

scholarly journals Primitive permutation groups and derangements of prime power order

2015 ◽  
Vol 150 (1-2) ◽  
pp. 255-291
Author(s):  
Timothy C. Burness ◽  
Hung P. Tong-Viet
Keyword(s):  
Prime Power ◽  
Permutation Groups ◽  
Prime Power Order

On Simply Transitive Primitive Permutation Groups

1969 ◽  
Vol 21 ◽  
pp. 1062-1068 ◽  
Author(s):  
R. D. Bercov
Keyword(s):  
Abelian Group ◽  
Direct Product ◽  
Prime Power ◽  
Direct Decomposition ◽  
Permutation Groups ◽  
Prime Power Order ◽  
Schur Ring ◽  
Abelian Subgroups ◽  
Prime 2

In (1) we considered finite primitive permutation groups G with regular abelian subgroups H satisfying the following hypothesis:(*) H = A × B × C, where A is cyclic of prime power order pα ≠ 4, B has exponent pβ < pα, and C has order prime to p.We remark that an abelian group fails to satisfy (*) (apart from the minor exception associated with the prime 2) if and only if it is the direct product of two subgroups of the same exponent.We showed in (1) that such a group G is doubly transitive unless it is the direct product of two or more subgroups each of the same order greater than 2. This was done by showing that (in the terminology of (3)) the existence of a non-trivial primitive Schur ring over H implies such a direct decomposition of H.

A GENERALIZED FIXED POINT FREE AUTOMORPHISM OF PRIME POWER ORDER

2012 ◽  
Vol 22 (04) ◽  
pp. 1250029
Author(s):  
GÜLİN ERCAN ◽  
İSMAİL Ş. GÜLOĞLU
Keyword(s):  
Fixed Point ◽  
Finite Group ◽  
Nilpotent Group ◽  
Prime Power ◽  
Prime Power Order ◽  
Nilpotent Length ◽  
A Finite Group

Let G be a finite group and α be an automorphism of G of order pn for an odd prime p. Suppose that α acts fixed point freely on every α-invariant p′-section of G, and acts trivially or exceptionally on every elementary abelian α-invariant p-section of G. It is proved that G is a solvable p-nilpotent group of nilpotent length at most n + 1, and this bound is best possible.

scholarly journals The energy of integral circulant graphs with prime power order

2011 ◽  
Vol 5 (1) ◽  
pp. 22-36 ◽  
Author(s):  
J.W. Sander ◽  
T. Sander
Keyword(s):  
Adjacency Matrix ◽  
Prime Power ◽  
Prime Power Order ◽  
Circulant Graph ◽  
Closed Formula ◽  
Circulant Graphs ◽  
Vertex Set

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. Such a graph can be characterized by its vertex count n and a set D of divisors of n such that its vertex set is Zn and its edge set is {{a,b} : a, b ? Zn; gcd(a-b, n)? D}. For an integral circulant graph on ps vertices, where p is a prime, we derive a closed formula for its energy in terms of n and D. Moreover, we study minimal and maximal energies for fixed ps and varying divisor sets D.

Space groups and groups of prime-power order II

1980 ◽  
Vol 35 (1) ◽  
pp. 203-209 ◽  
Author(s):  
H. Finken ◽  
J. Neub�ser ◽  
W. Plesken
Keyword(s):  
Prime Power ◽  
Prime Power Order ◽  
Space Groups

On S-Quasinormal and C-Normal Subgroups of Prime Power Order in Finite Groups

2011 ◽  
Vol 18 (04) ◽  
pp. 685-692
Author(s):  
Xuanli He ◽  
Shirong Li ◽  
Xiaochun Liu
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Prime Power ◽  
Maximal Subgroups ◽  
Prime Power Order ◽  
Normal Subgroups ◽  
A Finite Group

Let G be a finite group, p the smallest prime dividing the order of G, and P a Sylow p-subgroup of G with the smallest generator number d. Consider a set [Formula: see text] of maximal subgroups of P such that [Formula: see text]. It is shown that if every member [Formula: see text] of is either S-quasinormally embedded or C-normal in G, then G is p-nilpotent. As its applications, some further results are obtained.

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