MEXICO CITY (Reuters) -- Carlos Slim's brother interrogated leftist rebels for Mexico's intelligence agency while his eldest son often hands out a biographical novel about Leon Trotsky as a gift, according to a new book on the tycoon who was long the world's richest man. The biography, by far the most comprehensive written on Slim, seeks to show how the Mexico City businessman navigated local politics to become the world's richest man in a country where almost half the population lives in poverty.

Author Diego Enrique Osorno, a former reporter on the country's drug war for a Mexican national newspaper, spent more than seven years working on the book, which included three recent interviews with the telecoms magnate. However, it was not authorized by Slim. It is currently available only in Spanish.

Osorno compares Slim's three sons, who now run most of his businesses. The youngest, deeply Roman Catholic Patrick, part-financed a film about the 1920s Cristero War, which pitted the heirs of post-revolutionary Mexico against the church, and was part of a group that tried to start a new conservative political party.

In contrast, Slim's Formula One-loving eldest son Carlos likes to give away a novel about the assassination of exiled Russian Communist leader Trotsky in Mexico in 1940.

Middle son Marco Antonio, chairman of Slim's bank Grupo Financiero Inbursa and board member of BlackRock Inc., is the most discreet, and was frequently praised for his acuity by Slim in his interviews, Osorno said.

Slim's son-in-law and representative Arturo Elias said Carlos Jr. gives away many books, particularly Dale Carnegie's self-help tome "How to Stop Worrying and Start Living.” Elias said the family is not attached to a political party.

Osorno chronicles the family history, recounting how Slim's late wife was a cousin of Lebanese Presidents Bashir and Amin Gemayel and how his immigrant father arrived in Mexico from Lebanon to build his own sizable business.

Through freedom-of-information requests, he documents how Slim's brother Julian interrogated suspected leftist insurgents for Mexico's former intelligence agency DFS. Elias confirmed Julian worked at the DFS in the legal department. He did not know whether he was involved in interrogations.

And Osorno recounts the ups and downs of Slim's relationships with industry titans such as Cemex's Lorenzo Zambrano and Grupo Televisa Chairman Emilio Azcarraga.

Slim, 75, got along with the fellow tycoons until they stepped into his telecoms domain, as Zambrano and Azcarraga both did. The gradual souring of ties with Televisa culminated in Slim stopping advertising with the broadcaster in 2011.

(Reporting by Christine Murray; Editing by Dave Graham, Simon Gardner and Frances Kerry)