E-resources
Peer reviewed
Open access
-
Burness, Timothy C.; Lucchini, Andrea; Nemmi, Daniele
Journal of combinatorial theory. Series A, February 2023, 2023-02-00, Volume: 194Journal Article
Let G be a finite insoluble group with soluble radical R(G). In this paper we investigate the soluble graph of G, which is a natural generalisation of the widely studied commuting graph. Here the vertices are the elements in G∖R(G), with x adjacent to y if they generate a soluble subgroup of G. Our main result states that this graph is always connected and its diameter, denoted δS(G), is at most 5. More precisely, we show that δS(G)⩽3 if G is not almost simple and we obtain stronger bounds for various families of almost simple groups. For example, we will show that δS(Sn)=3 for all n⩾6. We also establish the existence of simple groups with δS(G)⩾4. For instance, we prove that δS(A2p+1)⩾4 for every Sophie Germain prime p⩾5, which demonstrates that our general upper bound of 5 is close to best possible. We conclude by briefly discussing some variations of the soluble graph construction and we present several open problems.
![loading ... loading ...](themes/default/img/ajax-loading.gif)
Shelf entry
Permalink
- URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year | Impact factor | Edition | Category | Classification | ||||
---|---|---|---|---|---|---|---|---|
JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
Select the library membership card:
If the library membership card is not in the list,
add a new one.
DRS, in which the journal is indexed
Database name | Field | Year |
---|
Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
---|
Source: Personal bibliographies
and: SICRIS
The material is available in full text. If you wish to order the material anyway, click the Continue button.