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On Arithmetic Functions of Finite Groups

Published online by Cambridge University Press:  17 April 2009

Ashish Kumar Das
Ashish Kumar Das
Affiliation:
Department of Mathematics, North Eastern Hill University, Permanent Campus, Shillong-793022, Meghalaya, India, e-mail: [email protected]
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The object of this paper is to develop and study group theoretic analogues of some of the fundamental concepts and results of arithmetic functions of positive integers.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 1 , February 2007 , pp. 45 - 58
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Apostol, T.M., Introduction to analytic number theory, Springer International Student Edition (Narosa Publishing House, New Delhi, 1993).Google Scholar
[2]Brodie, M.A., Chamberlain, R.F. and Kappe, L.-C., ‘Finite coverings by normal subgroups’, Proc. Amer. Math. Soc. 104 (1988), 669–674.CrossRefGoogle Scholar
[3]Cohen, E., ‘Arithemetical functions of finite abelian groups’, Math. Ann. 142 (1961), 165–182.CrossRefGoogle Scholar
[4]Delsarte, P.S., ‘Fonctions de Möbius sur les groupes abeliens finis’, Ann. of Math. 49 (1948), 600–609.CrossRefGoogle Scholar
[5]Jacobson, N., Basic algebra, vol I (W.H. Freeman and Company, U.S.A., 1974).Google Scholar
[6]Leinster, T., ‘Perfect number and groups’, arXiv:math.GR/0104012 v1 04 2001.Google Scholar
[7]Lucido, M.S. and Pournaki, M.R., ‘Elements with square roots in finite groups’, Algebra Colloq. 12 (2005), 677–690.CrossRefGoogle Scholar
[8]Mann, A., ‘Finite groups containing many involutions’, Proc. Amer. Math. Soc. 122 (1994), 383–326.CrossRefGoogle Scholar
[9]Marefat, Y., ‘Conjugacy structure type and degree structure type in finite p-groups’, Turkish J. Math. 24 (2000), 321–326.Google Scholar
[10]Menegazzo, F., ‘The number of generators of a finite group’, Irish Math. Soc. Bull. 50 (2003), 117–128.CrossRefGoogle Scholar