scholarly journals Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power order

2010 ◽  
Vol 3 (2) ◽  
pp. 201-214 ◽  
Author(s):  
Edward Dobson
Keyword(s):  
Prime Power ◽  
Automorphism Groups ◽  
Abelian Groups ◽  
Prime Power Order

scholarly journals On Keller's conjecture for certain cyclic groups

1979 ◽  
Vol 22 (1) ◽  
pp. 17-21 ◽  
Author(s):  
A. D. Sands
Keyword(s):  
Prime Power ◽  
Abelian Groups ◽  
Prime Power Order ◽  
Finite Abelian Groups ◽  
Cyclic Groups

Keller (6) considered a generalisation of a problem of Minkowski (7) concerning the filling of Rn by congruent cubes. Hajós (4) reduced Minkowski's conjecture to a problem concerning the factorization of finite abelian groups and then solved this problem. In a similar manner Hajós (5) reduced Keller's conjecture to a problem in the factorization of finite abelian groups, but this problem remains unsolved, in general. It occurs also as Problem 80 in Fuchs (3). Seitz (10) has obtained a solution for cyclic groups of prime power order. In this paper we present a solution for cyclic groups whose order is the product of two prime powers.

scholarly journals Lattice embeddings of abelian prime power groups

1997 ◽  
Vol 62 (2) ◽  
pp. 259-278 ◽  
Author(s):  
Roland Schmidt
Keyword(s):  
Direct Product ◽  
Prime Power ◽  
Abelian Groups ◽  
Subgroup Lattice ◽  
Prime Power Order

AbstractWe solve the following problem which was posed by Barnes in 1962. For which abelian groups G and H of the same prime power order is it possible to embed the subgroup lattice of G in that of H? It follows from Barnes' results and a theorem of Herrmann and Huhn that if there exists such an embedding and G contains three independent elements of order p2, then G and H are isomorphic. This reduces the problem to the case that G is the direct product of cyclic p-groups only two of which have order larger than p. We determine all groups H for which the desired embedding exists.

scholarly journals Automorphisms of Cayley graphs of metacyclic groups of prime-power order

2001 ◽  
Vol 71 (2) ◽  
pp. 223-232 ◽  
Author(s):  
Caiheng Li ◽  
Hyo-Seob Sim
Keyword(s):  
Graph Theory ◽  
Cayley Graph ◽  
Prime Power ◽  
Automorphism Groups ◽  
Cayley Graphs ◽  
Prime Power Order ◽  
Subsequent Work ◽  
Metacyclic Groups

AbstractThis paper inverstigates the automorphism groups of Cayley graphs of metracyclicp-gorups. A characterization is given of the automorphism groups of Cayley grahs of a metacyclicp-group for odd primep. In particular, a complete determiniation of the automophism group of a connected Cayley graph with valency less than 2pof a nonabelian metacyclicp-group is obtained as a consequence. In subsequent work, the result of this paper has been applied to solve several problems in graph theory.

The Homological Functors of Some Abelian Groups of Prime Power Order

2014 ◽  
Vol 71 (5) ◽  
Author(s):  
Rosita Zainal ◽  
Nor Muhainiah Mohd Ali ◽  
Nor Haniza Sarmin ◽  
Samad Rashid
Keyword(s):  
Tensor Product ◽  
Prime Power ◽  
Homotopy Theory ◽  
Abelian Groups ◽  
Prime Power Order ◽  
Schur Multiplier ◽  
Integer Coefficients ◽  
Nonabelian Tensor ◽  
Tensor Square ◽  
Special Case

The homological functors of a group were first introduced in homotopy theory. Some of the homological functors including the nonabelian tensor square and the Schur multiplier of abelian groups of prime power order are determined in this paper. The nonabelian tensor square of a group G introduced by Brown and Loday in 1987 is a special case of the nonabelian tensor product. Meanwhile, the Schur multiplier of G is the second cohomology with integer coefficients is named after Issai Schur. The aims of this paper are to determine the nonabelian tensor square and the Schur multiplier of abelian groups of order p5, where p is an odd prime

On the existence of semifields of prime power order admitting free automorphism groups

2007 ◽  
Vol 86 (1-2) ◽  
pp. 1-5 ◽  
Author(s):  
Mashhour Al-Ali Bani-Ata ◽  
Christoph Hering ◽  
Anni Neumann ◽  
Aymen Rawashdeh
Keyword(s):  
Prime Power ◽  
Automorphism Groups ◽  
Prime Power Order
Sign in / Sign up

Export Citation Format

Share Document