Equation 677 Database

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Magma 8672ebb21071…

magma 8672ebb21071
Size
451
Isomorphism class hash
8672ebb2107145c23ce72770c0e6f1904717a2b81c6356e58d791a7fdf0181d1
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: yes · rank: 441 (nullity 10) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 18:58:37
Display reorder
441,440,443,442,444,446,445,448,449,447,450,48,80,186,147,173,7,8,9,49,174,81,187,148,175,50,82,188,149,168,51,83,189,150,44,169,84,190,151,85,170,45,191,144,86,171,46,184,145,172,87,47,185,146,209,263,340,284,231,210,256,341,285,224,257,211,342,286,225,258,212,343,287,226,259,213,336,280,227,214,260,337,281,228,261,215,338,282,229,208,262,339,283,230,22,1,20,6,27,68,132,142,116,53,3,4,0,69,54,133,143,117,35,79,134,136,118,32,63,135,137,119,64,34,128,138,112,129,33,65,139,113,130,78,66,140,114,52,131,67,141,115,253,318,268,194,324,254,319,269,195,325,312,255,270,196,326,313,248,271,197,327,314,249,264,198,320,250,315,265,199,321,316,251,266,192,322,252,317,267,193,323,26,23,5,21,2,163,75,180,94,125,12,14,17,164,126,76,181,95,127,165,77,182,88,120,166,70,183,89,167,121,71,176,90,72,122,160,177,91,73,123,161,178,92,124,74,162,179,93,275,344,295,235,334,276,345,288,236,335,346,277,289,237,328,347,278,290,238,329,348,279,291,239,330,272,349,292,232,331,350,273,293,233,332,274,351,294,234,333,29,31,24,10,19,154,98,111,40,60,15,16,18,155,61,99,104,41,62,156,100,105,42,55,157,101,106,43,158,56,102,107,36,103,57,159,108,37,96,58,152,109,38,59,97,153,110,39,311,220,241,303,200,304,223,242,296,201,219,305,243,297,202,221,306,244,298,203,222,307,245,299,204,308,216,246,300,205,217,309,247,301,206,310,218,240,302,207,30,25,11,13,28,385,387,388,386,389,437,438,352,390,394,392,393,391,359,356,357,358,355,364,361,362,363,360,365,369,367,368,366,372,374,371,373,370,377,379,375,378,376,384,382,381,383,380,425,427,428,429,426,430,432,433,434,431,397,395,398,399,396,402,400,403,404,401,407,405,408,409,406,410,412,413,414,411,417,415,418,419,416,420,422,423,424,421,354,439,435,436,353 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 451 = 11 + 5*88, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#e876e21aad9bf541c6eb58d853b53a5ea16933d8d89788712e1cead26dc9fbcf, M = {88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 88): MacNeish's product over GF(8) x GF(11); GF(8) = F_2[x]/(x^3 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 11.

last edited by qawbecrdtey at 2026-10-07 18:58:38 · history