Equation 677 Database

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Magma adab40d20ea7…

magma adab40d20ea7
Size
707
Isomorphism class hash
adab40d20ea77c32a2b3a8295e635eac3be1fa5cfc69ff6068bdb4164ed11882
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 20:06:38
Display reorder
305,304,303,302,301,300,656,254,255,251,252,253,256,152,154,153,150,151,149,80,82,81,77,78,79,263,265,264,267,268,266,145,144,143,148,146,147,243,242,244,240,241,239,2,0,1,3,4,5,166,165,164,163,161,162,297,299,298,294,296,295,7,6,8,9,10,11,317,316,312,313,314,315,500,499,501,502,503,498,437,436,432,433,434,435,418,417,419,414,415,416,328,327,329,324,325,326,525,524,526,527,522,523,578,577,579,580,581,576,603,602,604,605,600,601,476,474,477,478,479,475,484,483,485,480,481,482,622,611,618,610,609,616,631,646,619,629,681,701,674,659,682,673,700,702,683,703,170,171,167,168,169,172,106,105,104,101,102,103,196,195,194,193,191,192,179,181,180,183,184,182,97,96,95,100,98,99,91,90,89,94,92,93,160,159,158,155,156,157,36,35,37,39,40,38,250,249,248,245,246,247,85,84,83,87,88,86,458,457,459,460,461,456,521,520,516,517,518,519,411,410,412,413,408,409,337,336,338,339,340,341,309,308,310,311,307,306,568,567,569,564,565,566,493,492,494,495,496,497,591,590,592,593,588,589,344,343,345,346,347,342,462,467,463,464,465,466,653,634,654,649,635,642,630,647,627,633,672,704,661,685,663,675,697,699,680,698,124,122,121,119,120,123,293,289,288,290,291,292,126,125,127,129,130,128,115,114,113,116,117,118,109,108,107,112,110,111,259,257,258,262,260,261,188,190,189,186,187,185,44,46,45,41,42,43,201,200,202,199,197,198,176,178,177,175,173,174,349,348,350,351,352,353,545,544,540,541,542,543,447,446,448,449,444,445,335,334,330,331,332,333,402,407,403,404,405,406,562,561,563,558,559,560,596,595,597,598,599,594,512,511,513,514,515,510,471,470,472,473,468,469,450,455,451,452,453,454,651,636,650,644,643,637,617,645,625,626,677,705,676,669,660,671,688,693,670,694,232,230,229,228,227,231,216,217,215,219,220,218,69,68,70,66,67,65,53,55,54,57,58,56,238,237,236,235,233,234,134,136,135,131,132,133,141,140,142,139,137,138,221,222,223,225,226,224,61,60,59,62,63,64,73,72,71,75,76,74,383,382,378,379,380,381,551,550,546,547,548,549,442,441,443,438,439,440,398,397,399,400,401,396,392,391,393,394,395,390,491,490,487,486,488,489,537,536,538,539,534,535,554,553,555,556,557,552,388,387,389,384,385,386,375,374,376,377,372,373,652,638,655,640,648,639,621,641,620,628,679,706,684,657,678,658,689,695,686,696,22,23,19,20,18,21,281,280,279,277,276,278,285,287,286,283,282,284,209,211,210,213,214,212,207,206,208,204,205,203,275,31,30,32,33,34,49,48,47,50,51,52,13,12,14,16,17,15,269,271,270,273,274,272,27,29,28,26,24,25,318,323,319,320,321,322,504,509,505,506,507,508,423,422,424,425,420,421,427,426,428,429,430,431,367,366,368,369,370,371,575,574,570,571,572,573,586,585,587,582,583,584,529,528,530,531,532,533,356,355,357,358,359,354,362,361,363,364,365,360,624,607,623,608,612,615,606,632,613,614,662,692,668,665,666,667,687,690,664,691 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#21508ce76d8339c8cc8a9db508194b7933fb8eb19570d11d640cb6bc14178d14, M = {54, 55, 56, 57, 58, 59, 128} 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 20:06:39 · history