Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771767 | Journal of Algebra | 2017 | 16 Pages |
Abstract
Let G be a finite 2-generated soluble group and suppose that ãa1,b1ã=ãa2,b2ã=G. Then there exist c1,c2 such that ãa1,c1ã=ãc1,c2ã=ãc2,a2ã=G. Equivalently, the subgraph Î(G) of the generating graph of a 2-generated finite soluble group G obtained by removing the isolated vertices has diameter at most 3. We construct a 2-generated group G of order 210â
32 for which this bound is sharp. However a stronger result holds if Gâ² has odd order or Gâ² is nilpotent: in this case there exists bâG with ãa1,bã=ãa2,bã=G.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Andrea Lucchini,