A Sampling of Remarkable Groups by Marianna C. Bonanome & Margaret H. Dean & Judith Putnam Dean

Author:Marianna C. Bonanome & Margaret H. Dean & Judith Putnam Dean
Language: eng
Format: epub
ISBN: 9783030019785
Publisher: Springer International Publishing

Try using this information to draw the directed edges of the Schreier graph. Your attempt may look something like the draft seen in Fig. 3.28.

Fig. 3.28Schreier graph of the Adding Machine for level 2

This draft can be improved with some rearrangement, as in Fig. 3.29. Cycling around the vertices, note how γ “adds 1” (modulo 4) to each binary string.

Fig. 3.29Schreier graph of the Adding Machine for level 2

Following the same procedure we can construct the Schreier graph for level 3. The vertices of the graph are labelled by 000, 001, 010, 011, 100, 101, 110, and 111. See Figs. 3.30 and 3.31.

Fig. 3.30Input/output of γ at level 3 of T

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