Since surviving last week's coup attempt, Turkish President Recep Tayyip Erdogan has escalated his battle against his arch-enemy, US-based Muslim preacher Fethullah Gulen whom he accuses of orchestrating the failed putsch.

Once close allies, the two fell out several years ago, and Erdogan now labels Gulen's supporters "terrorists" who run a shadowy "parallel state" in Turkey and tried to bring him down with military force.

Erdogan has demanded the extradition of the 75-year-old from the United States, where he lives in a wooded compound in Pennsylvania and, Gulen's followers say, leads a humble life, using nothing but a bedroom and a desk.

The usually-reclusive Gulen has emerged to condemn the coup and reject the accusations he was behind it as "ridiculous, irresponsible and false".

Erdogan has launched a sweeping purge of alleged "Gulenists", detaining or sacking over 50,000 soldiers, police, teachers and officials to cleanse the system of the Gulenist "virus".

What is Gulenism?

Gulen is the spiritual leader of the Hizmet (Service) movement, which is based on Sufi mysticism and promotes a moderate, tolerant Islam.

Gulenists, known for their piety and business acumen, say their faith advocates peace and harmony through hard work and altruism, and to merge a "civil Islam" with modernity, education and science.

The foundation runs private schools in Turkey, the US and some 150 other countries as well as a range of businesses, media outlets, cultural centres and think-tanks.

Gulen fled to the US in 1999 to escape charges of "anti-secular" activities, under what was then a secular administration that drew a strict line between mosque and state.

His followers, including loyal alumni from his schools, have been prominently placed in Turkey's military, police, justice apparatus and bureaucracy -- a group Erdogan now labels the "Fethullah Terrorist Organisation".

How did Erdogan and Gulen fall out?

Erdogan and Gulen were once close Islamic-conservative allies who transformed a political landscape that had for decades been the domain of secularists and coup-happy generals.

As Erdogan's Justice and Development Party (AKP) rose, Gulen's movement provided many of the technocrats to staff the bureaucracy.

But Erdogan became increasingly distrustful of Gulen, who has in turn accused Erdogan of seeking one-man rule.

The power struggle came to a head in late 2013 after judicial officials thought to be close to Gulen brought corruption charges that implicated some of Erdogan's inner circle, including his son Bilal.

Erdogan accused Gulenists of releasing embarrassing wiretaps and spreading them on social media.

In a series of counterattacks, he purged hundreds of army and police officers, and shut down thousands of Hizmet schools and newspapers believed to be sympathetic to his bitter rival.

How much power do Gulenists have?

Followers of Gulen have held prominent positions in Turkey's security and civil services, media and business -- although less so after the purges of recent years.

The extent of their influence and whether they work toward a common goal, however, remains subject of fierce debate.

Turkish state media Wednesday published what it said was the confession of a highly-placed Gulenist putschist, Lieutenant Colonel Levent Turkkan, who was the aide of Chief of General Staff Hulusi Akar.

The Anadolu news agency said Turkkan had admitted to being a member of Gulen's group, quoting him as saying: "I have obeyed the orders and instructions of the big brothers exactly."

Turkkan also said he had placed a recording device in the office of Akar's predecessor, Anadolu said.

The confession was deemed plausible by Jean-Francois Perouse, co-author of an Erdogan biography and researcher at the French Institute of Anatolian Studies in Istanbul.

He said Gulen had thousands of supporters in the administration but cautioned that the question is "to what extent that presence is accompanied by a very clear objective" with political ends.

How sweeping is the purge?

Since the failed coup, the government has arrested about 10,000 people and sacked or suspended tens of thousands more across the civil infrastructure, from army generals down to sports ministry officials and teachers.

Given the huge numbers, Perouse said those caught up must include a mix of "non-active supporters or alumni of the schools, for example, and people who are at the heart of the movement".

He said that, after the "cleansing" of the media and police, an army purge had been scheduled for early August, a threat that may explain the timing of the failed coup.

Political scientist Ahmet Insel said the Erdogan government knew who to strike against, also targeting justice officials it considered troublesome as it sought to "purify (the system) beyond Gulenist circles".

EU enlargement commissioner Johannes Hahn said earlier this week it appeared that the government had prepared -- even before the coup bid -- a list of people to be rounded up.