The abrupt removal of President Nikolai Podgorny from the Soviet Politburo last week shows that the struggle for the succession to Leonid Brezhnev as party secretary is beginning to weaken the inner core of the Kremlin leadership.

All the previous dismissals of Politburo members under the Brezhnev regime were designed to remove from the leadership the younger officials who might challenge the supremacy of the Brezhnev generation, now in its 70s. So long as this inner core held together, there was a good chance that the pressure from the younger leaders could be held in check. The sense of self-preservation therefore repeatedly led the older leaders into composing their policy differences, instead of fighting them out to the point at which one of them would have to be removed from the Politburo.

The senior member of this inner group, Mikhail Suslov, who is 75, has often taken a harder line than Brezhnev on foreign policy and has occasionally given signs that he opposes the stress on "consumerism" that is the hallmark of Brezhnev's domestic policies.

The signs that usually emerge from between the lines of official speeches have also made it possible to trace, over the years, the disagreements between Brezhnev and Premier Alexei Kosygin, now 73, on questions of economic policy. Manager of a vast government bureaucracy, Kosygin has often had to fight to preserve its autonomy against the encroachments of the party bureaucracy led by Brezhnev.

The day-to-day management of the party bureaucracy is exercised on Brezhnev's behalf by Andrei Kirilenko, his closest associate and, at 70 his equal in age. Podgorny was, at 74, most unlikely to challege Brezhnev for the succession - but, as president, he held a post that could become of crucial importance in the struggle for the succession. One analyst, Christian Duevel of Radio Liberty, who has traced the struggle between Podgorny and Brezhnev as it developed over the years, now speculates that Brezhnev wants the post for himself. But another possibility is that the vacancy is required for a younger mana whom Brezhnev wants to groom for the succession.

There is something to be said for both these eventualities. If Brezhnev's health is as poor as recent reports suggest, the assumption of the presidency would enable him to remain in the limelight without carrying the heavy burden that goes with his present post as party secretary. If the transition is carried out while he is still the effective leader of the party, he could try to ensure that the presidency carries with it more of a policy-making role than it has in the past.

But Brezhnev held the post of president for a time under the Khrushchev regime, and he used it to great advantage as a stepping stone to the position of the party's first secretary after he overthrew Khrushchev. The president did not give Brezhnev the power to challenge Khrushchev, but it did give him an opportunity to act on the national and international stage, to get his picture in the papers, to become a far more familiar figure than he had been previously - to be seen, in short, as the heir-apparent.

This made the transition to the Brezhnev regime much easier than it might otherwise have been. The dirty work involved in securing the removal of Khrushchev - who was enjoying a carefree holiday in the Crimea while his colleagues in Moscow were preparing the announcement of his dismissal - could not have been accomplished so easily if there had been no heir-apparent. Khrushchev's opponents would have had to agree on a successor before they took steps to remove him, which would have been difficult at the best of times, and particularly difficult when several ambitious politicians suddenly saw the chance of rising to the top position.

It could even be aruged that Khrushchev, by designating Brezhnev as his preferred successor, had sealed his own fate. It was a lesson that Brezhnev has certainly learned; for not only has he avoided designating a successor, he has also taken steps to ensure that none of the younger members of the Politburo are in a position to grab the limelight as he did under Khrushchev. Some of Brezhnev's policies have been strongly opposed by his associates during his tenure, and he probably owes his survival at least in part to the absence of a "natural" successor.

But if that is so, would Brezhnev designate a successor now by appointing a younger man to the presidency, and thus endanger his own chances of political survival? He certainly wants to stay on top long enough to earn his niche in history by arranging for the formal adoption of the "Brezhnev constitution," which is due to be passed at a special session of the supreme Soviet in October. By that time, too, if all goes well, a new strategic arms limitation agreement may be signed, to meet the deadline imposed by the expiration of the present agreement. That would fulfill another of Brezhnev's ambitions.

There may therefore be some substance to speculation that Brezhnev was really grooming himself to take over the presidency later in the year. Podgorny's dismissal may well be ascribed to his refusal to acquiesce in an arrangement that would have required him to vacate his post in the fall to make room for Brezhnev. But the departure of Podgorny now makes it necessary for Brezhnev either to take over his post much sooner than he might have intended or to appoint someone else to it. Both courses carry a risk that he has been careful to avoid in the past: They open up the whole question of the succession and thus make his own position less secure.

Brezhnev would have preferred Podgorny to stay as president for the time being. By forcing Brezhnev's hand, and bringing about his own abrupt dismissal, Podgorny has given a sign to younger men in the Politburo that it is time to begin actively campaigning - or, in Kremlin terms, intriguing - for the top post. He has also shown them that the unity of the Politburo's inner core is no longer inviolable and that they stand a good chance of breaching it if they work at it with sufficient determination.