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P. E. Dubuque (1937)
Sur le theoreme de FrobeniusMat. Sb., 2
W. K. Turkin (1931)
Generalisation du theoreme de FrobeniusAcademie des Sciences, Comptes Rendus, 193
J. Penot (1970)
Sur le théorème de FrobeniusBulletin de la Société Mathématique de France, 79
G. Miller (1942)
Some Deductions from Frobenius's Theorem.Proceedings of the National Academy of Sciences of the United States of America, 28 6
G. Hardy, By Hardy (1939)
An Introduction to the Theory of NumbersThe Mathematical Gazette, 23
L. Weisner (1925)
On the number of elements of a group which have a power in a given conjugate setBulletin of the American Mathematical Society, 31
Acta Mathematica Academiae Scientiarum Hungaricae Tomus 26 (1--2), (1975), 91--96. By H. S. FINKELSTEIN (Atlanta) In 1893 FROBENIUS [2] began an investigation of numerical properties associated with the solutions of the equation x"= 1 in a finite group. Then in 1925 WEISNER [8] obtained a divisor for the number of elements whose order is divisible by an integer k, if this number is not zero. The purpose of this paper is to consider a set of related group elements and investigate numerical relations which imply certain group-theoretic properties, namely cyclicity. I. Notation Throughout this paper G will denote a finite group of order IGI. If gEG, let o(g) denote the order of the element g. Let His, k]= {xEG: klo(x)[sk} where alb means a divides b, and let h[s, k]= IN[s, k]l, the size of the set H[s, k]. Let m~k= =max {d: disk, (d, k)=l}. If IGl=ft and (p, t)=l we write F/IGI. Let (p denote Euler's phi-function. [1. Divisibility conditions TURKIN [7] and DUBUQUE [1] considered the set H[s, k] and proved msk[h[s, k] and cp(k)lh[s, k] respectively. In general, the product rns~o(k ) is not a divisor of his, kl. LEMMA 1. G is cyclic if
Acta Mathematica Academiae Scientiarum Hungarica – Springer Journals
Published: May 21, 2016
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