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%I A079682
%S A079682 1,4,4096,590295810358705651712
%N A079682 Order of Burnside group B(4,n) of exponent 4 and rank n.
%C A079682 The Burnside group of exponent e and rank r is B(e,r) := F_r / N where 
               F_r is the free group generated by x_1, ..., x_r and N is the normal 
               subgroup generated by all z^e with z in F_r. The Burnside problem 
               is to determine when B(e,r) is finite.
%C A079682 B(1,r), B(2,r), B(3,r), B(4,r) and B(6,r) are all finite: |B(1,r)| = 
               r, |B(2,r)| = 2^r, |B(3,r)| = A051576, |B(4,r)| = A079682, |B(6,r)| 
               = A079683.
%C A079682 B(e,r) is infinite for e > 2 and n >= 13 (Ivanov).
%D A079682 M. Hall, Jr., The Theory of Groups, Macmillan, 1959, Chap. 18.
%D A079682 S. V. Ivanov, On the Burnside problem for groups of even exponent, Proc. 
               Internat. Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. 
               Math. 1998, Extra Vol. II, 67-75.
%D A079682 W. Magnus, A. Karrass and D. Solitar, Combinatorial Group Theory, Wiley, 
               1966, see p. 380.
%H A079682 J. J. O'Connor and E. F. Robertson, <a href="http://www-gap.dcs.st-and.ac.uk/
               ~history/HistTopics/Burnside_problem.html">History of the Burnside 
               Problem</a>
%H A079682 D. Rusin, <a href="http://www.math.niu.edu/~rusin/known-math/99/burnside">
               Burnside Problem</a>
%H A079682 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               BurnsideProblem.html">Burnside Problem</a>
%Y A079682 Sequence in context: A024061 A067482 A013830 this_sequence A127235 A102205 
               A046360
%Y A079682 Adjacent sequences: A079679 A079680 A079681 this_sequence A079683 A079684 
               A079685
%K A079682 nonn
%O A079682 0,2
%A A079682 N. J. A. Sloane (njas(AT)research.att.com), Jan 31 2003
%E A079682 The next term is 2^422.

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