There is no shortage of theories here today about the gangland execution of mob strongman Carmine Galante Thursday afternoon at a small Italian restaurant in Brooklyn.

There appears to be a consensus, though, that his murder may have been a group decision by other Mafia leaders, perhaps at the national level.

"You don't hit a boss without . . . approval," one federal source said. "We feel quite strongly that the decision was made here in New York. It could have been done by one guy after consulting with the others, or it could have been a decision involving all of the other families at the same time."

"It is quite possible that there was a conglomerate behind this," echoed James Sullivan, chief of detectives of the New York Police Department. "If it was a hit authorized by the appropriate people in the other crime families, then perhaps there will be no repercussions."

But Sullivan conceded that there were "mixed impressions" among homicide detectives FBI agents, Organized Crime Control Force members and members of the intelligence unit of the city police department who met today at the 90th Precinct police headquarters not far from the attack in which Galante and two other men were killed.

The second theory that has considerable currency is that Galante's murder was committedby "young Turks" from the Genovese family, the second largest of the five in New York City, which is now run by Frank Tieri.

Lt. Remo Franceschini, an organized crime expert said the killings appeared to be part of an underworld struggle for control of various rackets, including narcotics and prostitution. He said Galante was trying to cut into the Genovese family territory, and there were rumors that Tieri had put out a contract on Galante.

Polic have speculated that the murder last spring of one of Tieri's lieutenants, Pasquale Macchiarole, was part of this.

Then last Saturday, Macchiarole's 33-year-old son was killed at a bar he owned in Queens. This prompted further speculation today that hit men from the Genovese family may have accepted the contract to kill Galante in retaliation.

Police have put out an all-points bulletin for two Brooklyn men in their late twenties who reportedly were invited to the garden table where Galante, Leonardo Coppola, his 44-year-old associate, and Galante's cousin and owner of the restaurant, 47-year-old Giusseppe Turano, were slaughtered while eating lunch. Turano's 17-year-old son, John, was shot twice in the back while trying to hide from the gunmen.

Caesar Bonventre, 28, is believed to be a member of the Bonanno crime family, which Galante had controlled since Joseph Bonanno retired to Arizona over a decade ago. The second man, 27-year-old Baldo Amato, is unknown to federal authorities. Both men, however, have been arrested in the past by New York police on weapons charges.

There is widespread speculation that the two men, who sat on either side of Galante at Joe and Mary's Italian-American restaurant in the Bushwick section of Brooklyn, may have set him up for the killing.

Three men in ski masks came through the entrance to the restaurant shortly before 3 p.m. Thursday and went directly to the small garden in the rear where Galante and the others were drinking wine and eating fruit and salad.

The gunmen opened fire at close range with a shotgun and automatic pistols, killing Galante and Coppola instantly, and then disappeared in a car waiting outside.

Amato and Boventre apparently were not hit and also disappeared immediately.

"We don't know that they set him up," Sullivan said. But when asked by reporters why the two had not been shot along with Galante and the two other men at the table, Sullivan said, "You could draw assumptions from that."

The 69-year-old Galante had been involved in crime for almost six decades and had spent close to 20 years in prison, mainly on narcotics convictions. An old-style Mafia boss known for his ruthlessness, he was reputed to be personally responsible for scores of murders while he worked his way up the ladder of the Bonanno crime family.