They consist of a number of small, radical Islamic groups who have close connections - ideologically and militarily - with al Qaida. They are mostly former members of Hamas and Military Intelligence calls them "Afghans," and sometimes the "Palestinian Taliban," since their garb is like that of their counterparts in Afghanistan. The groups have a number of names. One is called the "Prophet's Sword," another the "Righteous Swords of Islam." Some of them hail from the infamous Durmush clan from the southern Gaza Strip, which established the Army of Islam, believed to be holding BBC reporter Alan Johnston and to have been involved in the abduction of Cpl. Gilad Schalit a year ago this week. Their goal, defense officials say, is to show that they are even more radical than Hamas, which they believe has transformed over the years from a religious movement into a nationalist one. These groups are believed to be behind the arson attacks on Internet cafes in Gaza in recent months. The Righteous Swords of Islam issued a death threat a few weeks ago against women working for the Palestinian Authority television station, accusing them of dressing immodestly and behaving "un-Muslim-like." The Shin Bet (Israel Security Agency) closely tracks these groups, which have recently strengthened their ties with global Jihadist elements in the Sinai Desert. Before Hamas's violent takeover of Gaza two weeks ago and the closure of the Rafah Crossing, they visited Gaza, apparently for the purpose of exchanging ideas on potential large-scale attacks against Israel. TWO TAPES were released this week - one video, the other audio. The first was of Johnston, who was seen wearing an explosive belt, warning Hamas not to storm the Durmush compound near Rafah, where the Palestinians believe he is being held captive. The second tape - and more significant for Israel - was the recording of Schalit that was posted on a Hamas Web site on Monday. It was essentially the first sign of life provided by his captors since he was kidnapped last June in an attack on his IDF position near Kerem Shalom. The Schalit tape did not tell Israel much. Before its release, the Shin Bet did not know where the abducted soldier was being held, and it probably still doesn't. But, even if it had known, the assumption within the defense establishment is that a covert rescue operation would be almost impossible in the densely populated Gaza Strip. For Hamas, however, releasing the Schalit recording had strategic importance. It hit the airwaves as Prime Minister Ehud Olmert and PA Chairman Mahmoud Abbas were meeting with Egyptian President Hosni Mubarak and Jordanian King Abdullah to discuss ways to revive the diplomatic process and to strengthen Abbas and Fatah in the wake of Hamas's Gaza conquest. Hamas's message was clear: to show that, in spite of the Sharm el-Sheikh summit, not only is it still a major political and diplomatic player, but that it holds the key to Schalit's release. Well, not exactly. While the tape seemed to indicate that Hamas was declaring exclusive responsibility and ownership over Schalit - in it, the soldier said he is being held by Izz a-Din al-Kassam - high-ranking defense officials said that at the end of the day a prisoner swap would have to be approved by the "Afghans." The groups, which essentially make up the Popular Resistance Committees, are as much responsible for Schalit's fate as Hamas is, say defense officials closely familiar with the dynamics of Gaza, and a deal cannot be reached without their permission. The Army of Islam was one of the groups which initially took responsibility for Schalit's kidnapping, and over the past year, reports have surfaced that the soldier was being held in the southern Gaza Strip by the Durmush clan. Though government officials expressed concern some months ago over the possibility that Mumtaz Durmush - the head of the clan - would not comply, when the time came, with a deal to release Schalit, today the growing assessment in the defense establishment is that if Hamas comes to him with a deal involving the release of some 1,000 Palestinian prisoners, he will have no choice but to let Schalit free. THE KEY to the deal is Egypt. Israel does not directly talk with Hamas, and it began using Egypt as its mediator immediately following the Second Lebanon War, when negotiations picked up speed. Egypt has several representatives in Israel. There are the officials from the Egyptian Embassy in Tel Aviv, some of whom are involved in dialogue, mostly between the PA and the Israeli government. And on the ground in Gaza, there is Gen. Mohammed Burhan, officially Cairo's security liaison to Gaza, who also serves as a secret mediator between Israel and Hamas. In spite of the increase in public calls for Olmert to make a prisoner swap as a result of the Schalit tape, defense officials this week said that it would still take time before the soldier was back at his parents' home in Mitzpe Hila. Israel is currently confronting Gaza with a two-pronged approach. On the one hand, it is hoping that Hamas means business by releasing the tape, and is pressing ahead with talks for Schalit's release. On the other hand, the IDF is continuing to operate in Gaza, as was demonstrated quite effectively on Wednesday during a 24-hour operation that killed 12 Palestinians. The operations - conducted in northern Gaza near the Karni Crossing and in southern Gaza on the outskirts of Khan Younis - are aimed at routing out Hamas and Islamic Jihad terrorists who, the IDF has noticed in recent weeks, have begun fortifying positions along the border fence with Israel. The goal is to prevent the border with Gaza from turning into what the border with Lebanon looked like in the six years preceding the Second Lebanon War last summer. There, Hizbullah had set up borderline posts and heavily-fortified bunker systems used as Katyusha rocket launching pads right under the IDF's nose. In both operations in Gaza on Wednesday, the troops only went two kilometers deep into the now Hamas-controlled territory, but it was sufficient to kill 12 Palestinians and wound 40, demonstrating that Hamas has been up to something along the border. A year after Schalit's kidnapping, the IDF fears that another abduction could be just around the corner. ON WEDNESDAY, while the Schalit tape was released and Olmert sat down in Sharm el-Sheikh for talks with Arab leaders, Minister of Strategic Affairs Avigdor Lieberman was traversing throughout Europe, talking to former and current leaders about his idea of deploying a multinational force, preferably from NATO, in the Gaza Strip. Lieberman met with former Spanish president Jose Maria Aznar, an outspoken advocate of Israel's joining NATO. He also met with NATO Deputy Secretary General Alessandro Minuto-Rizzo at headquarters in Brussels. One meeting that Lieberman didn't get was with John Colston, Assistant Secretary General for Defense Policy and Planning, who was in Israel last week for meetings at the IDF and Defense Ministry. It is unclear why Lieberman, who has made it his goal since joining the government to get Israel into NATO, didn't meet with Colston. Had he done so, however, he probably wouldn't have like what he would have heard. Calling for an increase in NATO-Israel relations, Colston told The Post that one of the most significant achievements during his visit was getting the IDF to agree tentatively to join NATO's "operational capabilities concept," a move that would open the door for potential Israeli participation in the alliance's global missions. Asked about a NATO force deploying in Gaza, Colston hinted at the difficulty involved, leading some to conclude he meant it would be almost impossible. First, NATO would need agreement from all parties involved (Hamas last week rejected the possibility). Then it would need to be asked to deploy there by the United Nations Security Council, which would require the consent of its 26 member states - no simple bureaucratic process. NATO, Colston said, does not have unlimited resources, and is already overextended in its operations in Afghanistan and Kosovo. "It won't happen," explained a senior Israeli defense official involved in the issue. "It will be very difficult to find European soldiers willing to come to Gaza to risk their lives." Then there is Lieberman's other agenda - getting Israel to join NATO. Here it looks as though he might actually have a better chance at succeeding, though maybe not for another decade or so. The Israeli government has yet to formulate official policy concerning NATO, and while the National Security Council is working on drafting such a paper, as usual, the more pressing issues like Schalit, Gaza, Lebanon and Syria will take precedence. Lieberman would do himself a favor by meeting with the Israeli officials involved in coordinating with NATO, some of whom - in the IDF and at the Defense and Foreign ministries - have been in their jobs for years, and are experts on the alliance's dynamics. These officials mostly agree that Israel would first have to resolve the Palestinian conflict before asking NATO for full-fledged membership; Colston himself hinted as much. With Hamas's takeover of Gaza, it looks like that will take awhile.