Equation 677 Database

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Magma b495d7302397…

magma b495d7302397
Size
765
Isomorphism class hash
b495d7302397c21d057e8f93d1ba1bc17b8b6f44bddf088e549fda3290da2a18
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 764) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 14:43:09
Display reorder
79,260,62,40,341,80,261,63,41,342,81,262,64,34,343,82,263,65,35,344,75,264,66,36,337,76,265,59,37,338,77,258,60,38,339,78,259,61,39,340,681,705,682,683,711,352,87,31,398,188,205,129,326,139,145,270,159,53,100,387,353,88,32,399,189,206,130,327,140,146,271,235,48,101,388,354,89,33,394,190,207,526,596,531,532,581,566,505,517,605,599,514,501,609,548,558,525,597,529,141,266,161,49,102,383,348,83,28,395,191,208,128,323,136,142,267,162,50,97,384,349,84,29,396,192,209,127,324,137,163,143,268,385,51,98,164,350,85,30,397,187,210,446,325,138,144,269,386,52,99,351,160,86,502,610,547,559,626,595,530,533,582,604,506,516,570,571,666,572,573,667,672,673,756,759,760,761,757,755,758,702,693,704,699,706,695,715,694,701,645,644,636,647,635,589,616,639,642,557,490,512,537,585,546,619,613,574,441,21,290,416,329,368,203,5,70,157,280,185,427,406,249,72,19,291,417,330,369,204,6,71,158,281,186,428,407,250,73,20,292,418,331,370,555,491,510,536,586,545,620,614,575,513,498,588,615,598,602,556,492,511,153,282,181,429,408,251,74,18,293,419,328,371,67,200,2,182,154,283,68,458,457,454,453,452,294,420,455,456,201,3,183,155,278,469,69,468,460,470,459,295,421,463,466,202,4,184,156,279,479,483,487,478,482,486,677,676,735,741,730,739,737,734,740,717,714,710,685,680,688,690,708,763,93,118,333,312,439,212,230,447,307,345,372,319,123,390,55,94,119,334,313,440,213,231,448,308,346,373,320,124,391,56,95,120,335,314,438,214,232,449,309,347,374,321,125,392,57,96,121,336,315,436,215,233,450,310,193,375,322,126,393,58,90,115,332,0,437,216,234,451,311,1,376,316,522,606,507,515,521,630,629,631,561,567,634,628,594,632,633,508,523,607,317,91,116,464,462,471,211,229,472,461,465,467,54,122,389,92,318,117,640,638,646,560,565,648,637,641,643,509,524,608,578,579,669,580,577,668,674,675,747,744,753,745,754,750,746,724,725,712,723,726,684,722,727,721,543,627,592,601,563,540,520,504,554,496,500,495,535,612,584,544,623,593,366,219,173,109,42,194,12,24,7,152,405,277,180,442,306,367,220,174,110,43,195,13,25,8,147,400,272,177,443,302,362,221,175,111,44,196,14,26,9,148,401,273,178,444,303,363,222,176,112,45,197,15,27,10,149,402,274,179,445,304,364,217,171,113,46,198,11,16,22,275,150,403,493,541,624,591,600,562,539,519,503,553,497,499,583,534,611,542,494,625,305,365,218,172,114,47,199,17,23,276,151,404,480,484,488,481,485,489,678,679,731,738,733,728,729,736,732,686,700,691,697,692,687,707,716,764,246,413,237,287,378,104,474,134,425,300,169,360,430,254,225,247,414,238,288,379,105,473,135,426,301,170,361,431,255,226,248,415,239,289,380,103,663,650,618,657,652,658,622,655,653,654,660,569,656,659,651,662,527,661,296,165,355,432,256,227,242,409,240,284,381,108,476,131,422,297,166,356,433,257,228,243,410,241,285,382,106,477,132,423,357,298,167,223,434,252,358,244,411,236,286,377,107,475,133,424,299,168,224,435,253,245,359,412,568,587,603,518,649,528,617,590,538,564,621,576,552,549,665,551,550,664,670,671,742,749,751,762,743,748,752,718,719,709,713,689,720,698,703,696 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 765 = 45 + 5*144, 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#28c135c31c9c16f63ac84541dde3ead566850ad6b588a124a02a031b47e5c71c, M = the submagma generated by {0, 7} (45 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, 144): MacNeish's product over GF(16) x GF(9); GF(16) = F_2[x]/(x^4 + x + 1), GF(9) = F_3[x]/(x^2 + 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 14:43:10 · history