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%I #24 Aug 12 2024 03:53:52
%S 1,2,4,2,4,2,8,2,2,8,2,4,8,2,2,4,8,2,2,4,16,2,2,2,4,16,2,2,4,4,16,2,2,
%T 2,4,4,16,2,2,2,4,8,16,2,2,2,2,4,8,16,2,2,2,4,4,8,16,2,2,2,2,4,4,8,16,
%U 2,2,2,2,4,4,8,32
%N Irregular triangular array read by rows. The n-th row gives the elementary divisors of the group of units in the quotient ring F_2[x]/<x^n>.
%C A general formula for the isomorphism class of the group of units in any quotient ring of the polynomial ring F_p[x] (p prime) is given by Keith Kearnes in the Mathematics Stack Exchange link below.
%H Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/1956919/multiplicative-group-modulo-polynomials">Multiplicative group modulo polynomials</a>.
%H Karlee Westrem, <a href="https://conservancy.umn.edu/server/api/core/bitstreams/56a0c4f3-1a9f-4e3d-a10a-bde8bcfc9dba/content"> Group of Units of Z_p[x] modulo f(x), Masters Thesis, University of Minnesota, 2020.
%e Triangle begins
%e 1;
%e 2;
%e 4;
%e 2, 4;
%e 2, 8;
%e 2, 2, 8;
%e 2, 4, 8;
%e 2, 2, 4, 8;
%e 2, 2, 4, 16;
%e 2, 2, 2, 4, 16;
%e 2, 2, 4, 4, 16;
%e 2, 2, 2, 4, 4, 16;
%e 2, 2, 2, 4, 8, 16;
%e 2, 2, 2, 2, 4, 8, 16;
%e 2, 2, 2, 4, 4, 8, 16;
%e 2, 2, 2, 2, 4, 4, 8, 16;
%e 2, 2, 2, 2, 4, 4, 8, 32;
%e ...
%t groupofunits2xn[e_] := Flatten[Table[{Table[2^(i + 1), {(Ceiling[e/2^i] - 2 Ceiling[e/2^(i + 1)] + Ceiling[e/2^(i + 2)])}]}, {i, 0, 10}]]; Prepend[Drop[Table[groupofunits2xn[n], {n, 1, 16}], 1], {1}]
%Y Cf. A375312.
%K nonn,tabf,new
%O 1,2
%A _Geoffrey Critzer_, Aug 11 2024
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