Groups as Graphs

Details Groups as Graphs Groups as Graphs

2009-06-28

arxiv.org/abs/0906.5144v1

Mathematics

General Mathematics

168 pages, 154 figures; Published by Editura CuArt, Romania in 2009

Scientific paper

For the first time we represent every finite group in the form of a graph in this book. The authors choose to call these graphs as identity graph, since the main role in obtaining the graph is played by the identity element of the group. This study is innovative because through this description one can immediately look at the graph and say the number of elements in the group G which are self-inversed. Also study of different properties, like the subgroups of a group, normal subgroups of a group, p-sylow subgroups of a group and conjugate elements of a group are carried out using the identity graph of the group in this book. This book has four chapters. The first chapter is introductory. The second chapter represents groups as graphs. In the third chapter, we have defined similar types of graphs for algebraic structures like commutative semigroups, loops, commutative groupoids and commutative rings. The final chapter poses 52 problems.

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