Arsenal, on present form, look far and away the best of the big four who habitually dominate the Premier League. Last Wednesday one saw them comfortably get the better of a much-respected Sevilla, even if they were assisted by a flagrant first own goal.

Yesterday, all too predictably they simply walked over poor, struggling Derby County. It was a case of the rapier against a bludgeon if you like, racehorses against dray horses.

Given Chelsea’s attempted hara-kiri last week following the Jose Mourinho affair, it is difficult to see on present form where the challenge,, at least in this country, is to come for the Gunners. This, even without the illustrious presence of Thierry Henry, whom Arsène Wenger after the Sevilla game confessed that he did not want to lose.

By way of substantial consolation, there is the form of the towering Toga international striker Emmanuel Adebayor, who is in ebullient form and who yesterday treated himself to a hat-trick, winning the admiration of both managers.

“A fantastic player,” enthused Billy Davies, the Derby manager. “Look at the pace and the physical power. Without doubt a fantastic striker and one of the best.”

Wenger added: “I feel that physically he looks stronger, and you see that in many challenges. He has a huge force coming out of him. Basically, he had that before, but he looks calm.”

The only drawback is that next year he will be up and away like other African stars in the Premier League to the African Cup of Nations. Some years ago, when he still owned Chelsea, I asked Ken Bates why he did not look for players in Africa and his reply was simply because they were so often unavailable.

But the transient star of the show yet again was the remarkable Cesc Fabregas. To speed of feet and thought, to a flair for the decisive pass, to a fiercely effective right-foot shot, he adds a precocious maturity. When Wenger let his talisman Patrick Vieira go, even he could hardly have expected, however much he hoped, that the so much smaller Fabregas would so dominate in midfield.

But dominate indeed he has and he would go on to score yet another of his spectacular right-footed goals. “I wanted to take him off,” admitted Wenger, “because he had a little calf problem at half-time. But he saw I wanted to take him off and he scored a great goal again.

“It’s amazing because it tells you how much of a physiological boost came from the goal he scored before. What strikes me is he is very hard with himself, naturally so, but he has his feet on the ground.” To coruscating effect. The goal with which he put Arsenal ahead last Wednesday against Sevilla was, it is true, a massively deflected kind of goal to shake the morale of even as good a team as the Spaniards. But most of his goals, and he is scoring far more frequently this season, need no deflection to help them fly home.

During last week, you felt that Davies had already resigned himself to a beating and even a battering when he praised Arsenal so fulsomely. He praised them again after this game, doing his best to brush aside defeat simply on the grounds that the Gunners are so strong. “You don’t expect anything at Arsenal,” he said. “It’s no embarrassment to lose and learn the lessons that we did today.”

Laborious, however, was the word for Derby yesterday and it was surprising that they never brought Robert Earnshaw, who one has seen produce such sparkling games for Wales, off the bench. Stephen Pearson did his best, but there was simply no subduing Fabregas, while a defence which stood off culpably on the occasion of the first Arsenal goal were far too heavy-footed to contain the red and white waves which swept down on them.

The first Arsenal goal came on 10 minutes. Fabregas found the lanky Abou Diaby on the left. He cut across as Derby retreated into the middle, then swept his right-footed shot into the top left-hand corner.

A couple of minutes later he was shooting again from the edge of the box, but Stephen Bywater dived full length to save. Arsenal appealed with some justice for a couple of penalties but in the event, Adebayor, who would convert one in the second half, did not make it 2-0 until the 25th minute, but once again he showed up the deficiencies of the Derby defence.

Latching onto Fabregas’s long ball he went almost contemptuously at speed through the centre of Derby’s defence, stepped around Bywater, and put the ball in the net.

Before half-time, when Fabregas took a right-wing corner, the lively little Eduardo, the Croatian-born Brazilian striker, beat the bigger Derby defenders to the ball for a header which Bywater turned over the top.

More goals for Arsenal had to come and they began to do so just four minutes into the second half. When Matt Oakley in desperation pulled Eduardo’s shirt, Adebayor coolly converted the penalty. As time went on, even the Arsenal centre-back Kolo Toure enthusiastically joined in attacks, and after one fine move, he headed Fabregas’s cross narrowly wide.

On 70 minutes Fabregas scored a dramatic goal. Toure was up there to service Eduardo, who cleverly kept possession and found Fabregas, who rocketed his shot into the top left-hand corner of the Derby goal. On 79 minutes, pursuing a long ball from Denilson, Adebayor shook off a tackle and placed his side-footed right-footer past the poor put-upon Bywater for Arsenal’s fifth.