On the Residual Properties of Generalized Direct Products of Groups

2020 ◽  
Vol 41 (9) ◽  
pp. 1704-1711
Author(s):  
E. A. Tumanova
Keyword(s):  
Direct Products ◽  
Residual Properties ◽  
Products Of Groups

scholarly journals Residual properties of graph products of groups

2016 ◽  
Vol 19 (2) ◽  
Author(s):  
Federico Berlai ◽  
Michal Ferov
Keyword(s):  
Direct Products ◽  
Graph Products ◽  
Amenable Groups ◽  
Residual Properties ◽  
Products Of Groups

AbstractWe prove that the class of residually 𝒞 groups is closed under taking graph products, provided that 𝒞 is closed under taking subgroups, finite direct products and that free-by-𝒞 groups are residually 𝒞. As a consequence, we show that local embeddability into various classes of groups is stable under graph products. In particular, we prove that graph products of residually amenable groups are residually amenable, and that the class of groups that are locally embeddable into amenable groups is closed under taking graph products.

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.

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