Equation 677 Database

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Magma b6bf039ff28e…

magma b6bf039ff28e
Size
707
Isomorphism class hash
b6bf039ff28e35bda17668e88c725e088a1c81763c3a97138055d77854c600bc
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 02:45:47
Display reorder
553,552,554,550,551,549,638,255,254,256,257,253,252,143,138,139,140,141,142,185,184,186,187,188,183,258,259,260,261,262,263,64,63,65,60,61,62,123,122,124,125,120,121,44,43,45,46,47,42,109,108,110,111,112,113,17,16,12,13,14,15,99,98,100,101,96,97,306,311,307,308,309,310,535,534,536,532,533,531,588,590,589,587,586,591,571,570,569,567,568,566,460,462,461,465,463,464,459,458,457,456,454,455,339,341,340,338,336,337,480,479,478,482,483,481,555,557,556,559,558,592,593,595,594,598,596,597,632,643,633,614,612,613,615,644,647,699,666,676,698,677,696,697,690,703,706,705,105,104,106,107,102,103,49,50,51,52,53,48,208,207,209,210,205,206,194,193,189,190,191,192,119,118,114,115,116,117,37,36,38,39,40,41,267,266,268,269,264,265,272,271,273,274,275,270,129,128,130,131,126,127,135,134,136,137,132,133,4,3,5,1,0,2,411,413,412,408,409,410,389,388,387,385,386,384,477,476,475,473,474,472,527,526,525,529,530,528,406,405,407,403,404,402,333,335,334,332,331,330,469,471,470,468,466,467,451,453,452,450,448,449,378,380,379,383,381,382,607,628,630,631,648,650,629,642,611,684,683,692,675,663,670,674,669,682,695,701,278,277,279,280,281,276,95,90,91,92,93,94,24,29,25,26,27,28,285,284,286,287,282,283,89,88,84,85,86,87,18,23,19,20,21,22,81,80,82,83,78,79,161,160,156,157,158,159,35,34,30,31,32,33,236,235,237,238,239,234,247,246,248,249,250,251,573,422,423,420,421,419,373,372,374,375,376,377,426,425,424,428,429,427,514,513,515,516,517,518,495,494,493,492,490,491,605,604,603,601,602,600,430,432,431,435,433,434,498,497,496,500,501,499,512,511,510,508,509,572,622,646,626,645,625,608,618,609,617,693,680,687,686,664,665,679,657,691,681,700,167,166,162,163,164,165,11,6,7,8,9,10,72,77,73,74,75,76,300,301,302,303,304,305,244,243,245,240,241,242,313,312,314,315,316,317,298,297,299,294,295,296,66,71,67,68,69,70,147,146,148,149,144,145,152,151,153,154,155,150,288,293,289,290,291,292,371,370,369,368,366,367,439,441,440,438,436,437,524,523,522,520,521,519,548,547,546,544,545,543,400,399,401,397,398,396,361,360,362,363,364,365,345,347,346,344,342,343,506,505,507,502,503,504,538,537,539,540,541,542,623,624,606,621,616,620,619,651,649,702,672,685,704,658,667,678,659,694,688,689,199,198,200,195,196,197,181,182,229,222,180,230,202,231,203,204,223,201,226,225,227,232,228,233,326,328,327,324,325,329,178,177,179,174,175,176,172,171,173,168,169,170,322,321,323,319,318,320,212,211,213,214,215,216,217,224,218,219,220,221,54,59,55,56,57,58,392,391,390,395,393,394,417,416,418,414,415,599,562,561,560,564,565,563,484,486,485,489,487,488,580,582,581,583,584,585,579,578,577,575,576,574,348,350,349,353,351,352,358,357,359,354,355,356,443,442,444,445,446,447,641,627,639,640,635,634,610,636,637,671,656,661,673,652,653,655,654,660,662,668 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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#5ad34b2f8758383b4965947b4701d5813e2a88f030dcc851453e9c1dba339352, M = {120, 121, 122, 123, 124, 125, 134} 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, 140): MacNeish's product over GF(4) x GF(5) x GF(7); GF(4) = F_2[x]/(x^2 + 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: 101.

last edited by qawbecrdtey at 2026-10-07 02:45:49 · history