23 examples
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- Building on this result, the conjecture holds if G is a classical group.
- It is not yet known whether the Novikov conjecture holds true for all groups.
- Let us see whether this reasonable conjecture holds good. Cited from Folklore as an Historical Science, by George Laurence Gomme
- It is difficult to verify whether the conjecture holds for a given balanced presentation or not.
- Later Quinn completed the proof that the characterization conjecture holds in full generality.
- The conjecture holds in many partial cases, see for instance, Kari and Trahtman.
- Finally, it was shown later that any model of ZFC in which the conjecture holds, implies the existence of a model with a large cardinal.
- It is an open problem whether it is decidable, but if Schanuel's conjecture holds then the decidability of this theory would follow.
- If the Galois group is supersolvable then all representations are of this form so the Artin conjecture holds.
- The conjecture holds for a finite field by Quillen's computations of the K-groups in this case.
- It has been verified that Jacobson's conjecture holds in Noetherian serial rings.
- The Pacman Conjecture holds that durable goods monopolists have complete market power and so can exercise perfect price discrimination, thus extracting the total surplus.
- If the Hodge standard conjecture holds, then the Lefschetz conjecture and Conjecture D are equivalent.
- In particular the Kummer-Vandiver conjecture holds for regular primes.
- The conjecture holds only when there is an infinite time horizon, as otherwise a possible action for the monopolist would be to announce a very high price until the second to last period, and then sell at the static monopoly price in the last period.
- Stong has shown that the conjecture holds for the Cayley graph of the wreath product Z m wr Z n with the natural minimal generating set when m is either even or three.
- If it holds, then the Lefschetz conjecture implies Conjecture D. In characteristic zero the Hodge standard conjecture holds, being a consequence of Hodge theory.
- One conjecture holds that Mormon settlers also strongly objected to the profitable traditional trade in native slaves and interfered in many transactions, although this would seem to be contradicted by the fact that Brigham Young was not, by his own account, an abolitionist.
- The advantage of the Cayley graph formulation is that such graphs correspond to a finite group G and a generating set S, Thus one can ask for which G and S the conjecture holds rather than attack it in full generality.
- The date of revision and the identity of the reviser are equally unknown, though a reasonable conjecture holds that the revision was likely done just before the 1633 revival of the play by the King's Men, when the play was acted in conjunction with Shakespeare's.