Primitive Permutation Groups Containing a Cycle of Prime Power Length

1978 ◽  
Vol 10 (3) ◽  
pp. 256-260 ◽  
Author(s):  
Richard Levingston
Keyword(s):  
Prime Power ◽  
Permutation Groups

scholarly journals A Note on Primitive Permutation Groups of Prime Power Degree

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
Qian Cai ◽  
Hua Zhang
Keyword(s):  
Prime Power ◽  
Permutation Groups ◽  
Simple Type ◽  
Present Stage ◽  
Primitive Groups ◽  
Short Survey ◽  
Product Action ◽  
Action Type ◽  
Affine Type

Primitive permutation groups of prime power degree are known to be affine type, almost simple type, and product action type. At the present stage finding an explicit classification of primitive groups of affine type seems untractable, while the product action type can usually be reduced to almost simple type. In this paper, we present a short survey of the development of primitive groups of prime power degree, together with a brief description on such groups.

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

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

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.

IRREDUCIBLE MONOMIAL LINEAR GROUPS OF DEGREE FOUR OVER FINITE FIELDS

2004 ◽  
Vol 14 (03) ◽  
pp. 253-294 ◽  
Author(s):  
D. L. FLANNERY
Keyword(s):  
Finite Fields ◽  
Prime Power ◽  
Final Section ◽  
Permutation Groups ◽  
Linear Groups

We describe an algorithm for explicitly listing the irreducible monomial subgroups of GL (n,q), given a suitable list of finite irreducible monomial subgroups of [Formula: see text], where n is 4 or a prime, and q is a prime power. Particular attention is paid to the case n=4, and the algorithm is illustrated for n=4 and q=5. Certain primitive permutation groups can be constructed from a list of irreducible monomial subgroups of GL (n,q). The paper's final section shows that the computation of automorphisms of such permutation groups reduces mainly to computation of irreducible monomial subgroups of GL (n,q), q prime.

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