scholarly journals Homomorphisms on infinite direct products of groups, rings and monoids

2015 ◽  
Vol 274 (2) ◽  
pp. 451-495 ◽  
Author(s):  
George Bergman
Keyword(s):  
Direct Products ◽  
Products Of Groups

On graphical regular representations of direct products of groups

1972 ◽  
Vol 76 (2) ◽  
pp. 168-171 ◽  
Author(s):  
Mark E. Watkins ◽  
Lewis A. Nowitz
Keyword(s):  
Direct Products ◽  
Regular Representations ◽  
Products Of Groups

scholarly journals A new graph over semi-direct products of groups

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 611-619
Author(s):  
Sercan Topkaya ◽  
Sinan Cevik
Keyword(s):  
Chromatic Number ◽  
Final Section ◽  
Degree Sequence ◽  
Domination Number ◽  
Clique Number ◽  
Perfect Graph ◽  
Direct Products ◽  
Products Of Groups ◽  
Minimum Degrees ◽  
Product Of Groups

In this paper, by establishing a new graph ?(G) over the semi-direct product of groups, we will first state and prove some graph-theoretical properties, namely, diameter, maximum and minimum degrees, girth, degree sequence, domination number, chromatic number, clique number of ?(G). In the final section we will show that ?(G) is actually a perfect graph.

A Note on Generalized Direct Products of Groups

1973 ◽  
Vol 25 (1) ◽  
pp. 115-116
Author(s):  
Marlene Schick
Keyword(s):  
Direct Product ◽  
Direct Products ◽  
Compatibility Conditions ◽  
Cyclic Groups ◽  
Products Of Groups ◽  
Finite Set

In [1] Tang proved that the generalized direct product of a finite set of cyclic groups amalgamating subgroups which satisfy certain compatibility conditions always exists. In the proof, Theorem 4.1 is made use of. However, this theorem is not correct since we can construct examples of groups which satisfy the conditions of Theorem 4.1, but whose generalized direct product does not exist. Therefore, a modification of this result as pointed out by Professor Tang is given here, together with the resulting modification of the proof of the result stated above.

scholarly journals Presentations for some direct products of groups

1983 ◽  
Vol 28 (1) ◽  
pp. 131-133 ◽  
Author(s):  
P.E. Kenne
Keyword(s):  
Direct Product ◽  
Alternating Group ◽  
Direct Products ◽  
Icosahedral Group ◽  
Products Of Groups

We give efficient presentations for the direct product of two copies of the alternating group of degree five and the direct product of the alternating group of degree five and the binary icosahedral group.

On the Automorphism Group of Direct Products of Groups with Finite Exponent

2021 ◽  
Vol 128 (2) ◽  
pp. 168-173
Author(s):  
Dorin Andrica ◽  
Sorin Rădulescu ◽  
George C. Ţurcaş
Keyword(s):  
Automorphism Group ◽  
Direct Products ◽  
Products Of Groups ◽  
Finite Exponent
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