In particular, suspicions centre on the Ulster Defence Association, one of the two major loyalist paramilitary groupings which are supposed to be on ceasefire.
The theory runs that only the UDA, a long-established organisation, had the capacity to make a bomb of the type which killed Mrs Nelson.
Only one person has been killed by a loyalist under-car bobby trap device of the type used yesterday: loyalist figure Glen Greer, who was killed in 1997. That attack was the work of the UDA.
The RUC will now be concentrating one of its main lines of inquiry on whether the UDA as an organisation, or individual members within it, aided the Red Hand Defenders in the Nelson killing.
If UDA involvement does emerge, alarm bells will ring because it's ceasefire, which has been in existence since 1994, has been a major figure in reducing the Northern Ireland casualty lists to their present low levels.
The Red Hand Defenders, who were banned last month by the Secretary of State for Northern Ireland, Mo Mowlam, have been responsible for two killings in recent months.
One was that of a Catholic man shot dead in North Belfast while the other was that of a Catholic police officer hit in the face by a crude blast bomb during a loyalist marching protest.There have been recent concerns that the UDA was showing signs of becoming detached from the peace process.
The grouping has found itself out in the cold of late, since representatives of its political wing failed to win seats in the Belfast assembly.
The fear has been that without a political anchor it might drift away from the peace process and return to killings.
Loyalists have in recent months been the main source of violence in Northern Ireland. They have carried out roughly the same number of "punishment" attacks as the IRA, and have also petrol-bombed several dozen Catholic homes.
The level of killings has by Northern Ireland standards been low, loyalists have been responsible for three of the four deaths since last September. Two of these were carried out by a small splinter group, the Red Hand Defenders.
But although this group has some guns, most of its attacks so far have been carried out using crude petrol-bombs or pipe-bombs.
The question therefore arises of whether it had the capacity to make a device such as that which killed Mrs Nelson. The UDA has in the past used such devices.
There is also a historical pointer towards the UDA, in that the organisation was responsible for the killing in 1989 of the solicitor Pat Finucane, who, like Mrs Nelson, was viewed as a highly effective advocate for nationalists and republicans.
Mr Finucane's case remains a political issue, with allegations of official collusion gathering ground. Only last month more than a thousand legal figures from all over the world signed a petition calling for an investigation into his death.
Last night republicans and nationalists were already alleging security force involvement in Mrs Nelson's murder. Her killing seems destined to join that of Mr Finucane in the annals of the many cases accruing more and more allegations as the years pass.Reuse content