Hall formula for abelian groups

introduction

• "The sum of the reciprocals of the orders of all the Abelian groups of order a power of p is equal to the sum of the reciprocals of the orders of their groups of automorphisms."

memo

• https://books.google.com.au/books?id=Snecq4MHl8YC&pg=PA32&lpg=PA32&dq=Philip+Hall%27s+%27rather+curious%27+formula&source=bl&ots=cQPIExHEaL&sig=139v18ME5cTVIyAvqcVCUcX8lfE&hl=en&sa=X&ei=YE1ZVdXwIMzs8AXByoLgAg&ved=0CCoQ6AEwAg#v=onepage&q=Philip%20Hall%27s%20%27rather%20curious%27%20formula&f=false

encyclopedia

• http://en.wikipedia.org/wiki/Hall_algebra

articles

• Mann, Avinoam. ‘Philip Hall’s “Rather Curious” Formula and the Rogers-Ramanujan Identities’. arXiv:1505.02369 [math], 10 May 2015. http://arxiv.org/abs/1505.02369.
• Mann, Avinoam. ‘Philip Hall’s “rather Curious” Formula for Abelianp-Groups’. Israel Journal of Mathematics 96, no. 2 (1 June 1996): 445–48. doi:10.1007/BF02937316.