Prime Power Indices in Factorised Groups
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DOI: 10.1007/s00009-017-1023-6
Abstract: Let the group $$G=AB$$G=AB be the product of the subgroups A and B. We determine some structural properties of G when the p-elements in $$A\cup B$$A∪B have prime power indices in G, for some prime… read more here.
Keywords: power indices; power; indices factorised; prime power ... See more keywords
On the number of derangements and derangements of prime power order of the affine general linear groups
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DOI: 10.1007/s10801-016-0709-3
Abstract: A derangement is a permutation that has no fixed points. In this paper, we are interested in the proportion of derangements of the finite affine general linear groups. We prove a remarkably simple and explicit… read more here.
Keywords: derangements prime; linear groups; power order; general linear ... See more keywords
Generalized cyclotomic numbers and cyclic codes of prime power length over Z4
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DOI: 10.1142/s1793557119500852
Abstract: Generalized cyclotomic numbers of order [Formula: see text] with respect to an odd prime power are obtained. Hence, explicit expressions for primitive idempotents in the ring [Formula: see text] are obtained in two cases, when… read more here.
Keywords: cyclotomic numbers; prime power; generalized cyclotomic; formula see ... See more keywords
Sums of one prime power and two squares of primes in short intervals
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DOI: 10.1216/rmj.2021.51.213
Abstract: Let k≥1 be an integer. We prove that a suitable asymptotic formula for the average number of representations of integers n=p1k+p22+p32, where p1, p2, p3 are prime numbers, holds in intervals shorter than the ones… read more here.
Keywords: squares primes; prime power; sums one; two squares ... See more keywords