Equation 677 Database

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Magma fc66a181aa1e…

magma fc66a181aa1e
Size
595
Isomorphism class hash
fc66a181aa1e0e5781b6bad32eee2b7f2b7b9e61658877d86f4fc2ad2eae7bfc
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 20:43:09
Display reorder
82,81,84,85,86,83,119,118,120,121,116,117,123,122,124,125,126,127,63,62,58,59,60,61,456,457,458,459,460,461,527,582,564,570,577,207,206,165,208,209,210,178,149,145,146,147,148,48,47,49,50,51,46,0,2,1,182,181,156,203,205,204,164,114,115,25,24,21,22,23,183,175,236,233,234,235,176,218,217,219,168,215,216,354,353,355,357,358,356,494,493,492,495,496,497,319,318,317,320,321,322,486,488,487,490,491,489,418,417,416,413,414,415,296,295,297,298,294,293,333,332,334,329,330,331,440,439,438,441,442,443,550,549,536,538,534,533,535,537,576,590,559,556,575,555,553,579,10,9,11,12,13,14,54,53,55,56,57,52,91,90,92,87,88,89,100,99,101,102,103,104,75,74,76,71,72,73,34,33,35,36,32,184,199,163,200,201,202,162,250,249,180,251,247,248,365,367,366,368,369,370,302,304,303,300,301,299,395,397,396,399,400,398,348,347,349,352,350,351,509,506,507,508,504,499,274,273,275,271,272,270,306,305,307,308,309,310,498,502,500,505,501,503,520,517,525,548,547,530,529,528,551,565,567,580,566,573,572,593,45,44,40,41,42,43,31,30,26,27,28,29,4,3,5,6,7,8,19,18,20,15,16,17,97,96,98,93,94,95,152,151,153,154,155,263,257,253,258,259,260,246,256,255,252,261,262,254,455,454,453,452,450,451,376,375,374,371,372,373,412,411,410,407,408,409,291,290,292,289,287,288,364,363,362,359,360,361,315,314,316,312,313,311,404,406,405,403,401,402,338,340,339,336,337,335,541,532,521,514,513,524,515,522,557,554,560,552,568,592,594,558,140,139,141,142,143,144,64,190,187,188,158,189,223,170,220,169,221,222,198,197,161,105,106,107,79,78,80,77,191,192,173,232,229,230,174,231,160,196,193,194,195,159,238,237,239,177,240,241,392,394,393,389,390,391,469,468,470,473,471,472,437,277,276,278,279,280,483,485,484,481,482,480,446,445,444,447,448,449,379,378,377,382,380,381,384,383,385,386,387,388,343,342,341,344,345,346,546,543,519,510,518,511,512,516,587,562,583,571,563,569,588,589,70,69,65,66,67,68,150,244,245,179,242,243,212,167,213,214,166,211,186,185,157,37,38,39,130,129,131,128,225,224,227,226,171,228,172,132,136,135,137,138,133,134,108,113,109,110,111,112,282,281,283,285,286,284,426,425,427,430,428,429,324,323,325,328,326,327,419,421,420,423,424,422,463,464,462,466,467,465,264,265,266,268,269,267,436,435,434,432,433,431,479,478,477,474,475,476,539,523,526,545,544,542,531,540,561,591,578,581,584,586,585,574 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#83fb73755ed07f789756511d0e776415c2bd28bb0aaa387c6c265081499d5ced, M = the submagma generated by {0, 12} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 20:43:10 · history