On The Number of Groups of Squarefree Order

M. Ram Murty, Srimeenakshi Srinivasan

Type: Article

Publication Date: 1987-12-01

Citations: 6

DOI: https://doi.org/10.4153/cmb-1987-061-x

Abstract

Abstract Let G ( n ) denote the number of non-isomorphic groups of order n . We prove that for squarefree integers n , there is a constant A such that where denotes the Euler function. This upper bound is essentially best possible, apart from the constant A .

Locations

Canadian Mathematical Bulletin - View - PDF

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Action	Title	Year	Authors
+ PDF Chat	On the Average Number of Groups of Square-Free Order	1987	Carl Pomerance
+ PDF Chat	On the average number of groups of square-free order	1987	Carl Pomerance
+	Groups of a Square-Free Order	2010	Iordan Ganev
+	Group Enumeration and Where It Leads Us	1998	L. Pyber
+	Counting Finite Groups	1996	M. Ram Murty
+	MT300: Groups of a Square-Free Order	2010	Iordan Ganev Updated January

Works Cited by This (6)

Action	Title	Year	Authors
+	�ber die Anzahl der Teiler einer nat�rlichen Zahl, welche die Formp?1 haben	1955	K. Prachar
+ PDF Chat	On the average number of groups of square-free order	1987	Carl Pomerance
+	On the number of groups of a given order	1984	M. Ram Murty V. Kumar Murty
+	On the enumeration of finite groups	1987	Paul Erdős M. Ram Murty V. Kumar Murty
+	AN ENUMERATION THEOREM FOR FINITE GROUPS	1969	Peter Neumann
+	On Distinguishing Prime Numbers from Composite Numbers	1983	Leonard M. Adleman Carl Pomerance Robert Rumely