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Parity Theorem for Permutations - References

John O. Kiltinen

Bartlow, T. L. (1972), “An Historical Note on the Parity of Permutations,” American Mathematical Monthly, Vol. 79, No. 7, 766-769.

Brenner, J. L. (1957), “A New Proof That No Permutation is Both Even and Odd,” American Mathematical Monthly, Vol. 64, No. 7, 499-500.

Burns, J. E. (1913), “The Foundation Period in the History of Group Theory,” American Mathematical Monthly, Vol. 20, No. 5, 141-148.

Cauchy, A.-L. (1815), “Mémoire sur les fonctions qui ne peuvent obtenir que deux valeurs égale et de signes contraires par suite des transposition opérées entre les variables qu’elles renferment,” J. de l’École polytechnique, Vol. 10, 29-112; Oeuvres Complètes, ser II. vol. pp. 91-169.

Fraleigh, J. B. (1982), A First Course in Abstract Algebra, 3rd ed., Addison-Wesley.

Gallian, J. A. (1998), Contemporary Abstract Algebra, 4th edition, Houghton-Mifflin.

Gray, E. L. (1963), “An Alternative Proof for the Invariance of Parity of a Permutation Written as a Product of Transpositions,” American Mathematical Monthly, Vol. 70, No. 9, 995.

Hall, F. M. (1966), An Introduction to Abstract Algebra, Cambridge University Press.

Halperin, I. (1960), “Odd and Even Permutations,” Canadian Math. Bulletin, Vol. 3, 185-186.

Herstein, I. N. (1964), Topics in Algebra, Blaisdell Publishing Company.

Herstein, I. N. (1986), Abstract Algebra, Macmillan.

Higgs, D., and P. de Witte, (1979), “On Products of Transpositions and Their Graphs,” American Mathematical Monthly, Vol. 86, No. 5, 376-380.

Kiltinen, J. O. (in preparation), Oval Track and Other Permutation Puzzles (And Just Enough Group Theory to Solve Them), book and software package.

Kleiner, I. (1986), “The Evolution of Group Theory,” Mathematics Magazine , Vol. 59, No. 4, 195-213.

Liebeck, H. (1969), “Even and Odd Permutations,” American Mathematical Monthly, Vol. 76, No. 6, 668.

Miller, W. I. (1971), “Even and Odd Permutations,” American Mathematical Association of Two-Year Colleges Journal, Vol. 5, 32.

Nelson, S. (1987), “Defining the Sign of a Permutation,” American Mathematical Monthly, Vol. 94, No. 6, 543-545.

Phillips, T. W. (1967), “On the Definition of Even and Odd Permutations,” American Mathematical Monthly, Vol. 74, No. 10, 1249-1251.

Saracino, D. (1980), Abstract Algebra: A First Course, Addison-Wesley.

Spitznagel, E. L., Jr., (1968), “Note on the Alternating Group,” American Mathematical Monthly, Vol. 75, No. 1, 68-69.

Weil, C. E. (1964), “Another Approach to the Alternating Subgroup of the Symmetric Group,” American Mathematical Monthly, Vol. 71, No. 5, 545-546.

John O. Kiltinen, " Parity Theorem for Permutations - References," Convergence (December 2004)