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Galileo and the modern concept of infinity

Edward Kasner
1905 Bulletin of the American Mathematical Society  
1905.] THE CONCEPT OF INFINITY. 499 of the orders 4 and 8. Hence, there are just four groups in which H is necessarily non-abelian. In two of these GjA is cyclic while the quotient group is non-cyclic in the other two. The total number of the non-abelian groups of order 2 m which contain an invariant cyclic subgroup of order 2 m~2 , but no such subgroup of order 2 m_1 is therefore fourteen. The last four were explicitly excluded from my list of these groups which do not contain an abelian
more » ... in an abelian subgroup of order 2 m_1 including A * since Burnside had considered this subject. Knowing that Burnside gave the correct number of these groups I failed to observe the compensating errors. It may be added that the title of Hallet's paper as given in both reports noted above is misleading, since every possible group of order 2 m contains an invariant subgroup of order 2 m~2 .
doi:10.1090/s0002-9904-1905-01253-2 fatcat:3rybzo3xcbbodf5nhg3ka5rmka