Equation 677 Database

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Magma 39532c8d2112…

magma 39532c8d2112
Size
941
Isomorphism class hash
39532c8d2112bb660b288a1d7ad300aaee3fc8726415dd40ceaa45468b5f3168
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 940) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 19:45:25
Display reorder
940,814,82,72,88,503,626,409,759,487,749,610,403,743,393,616,509,765,387,493,632,815,83,73,89,496,627,410,752,480,750,611,404,736,394,617,510,766,388,494,633,808,84,74,90,497,628,411,753,481,751,612,405,737,395,618,511,767,389,495,634,809,85,75,91,498,629,412,754,482,744,613,406,738,396,619,504,760,390,488,635,810,86,76,92,499,630,413,755,483,745,614,407,739,397,620,505,761,391,489,636,811,87,77,93,500,631,414,756,484,746,615,400,506,740,398,621,637,762,384,490,507,80,812,78,94,501,624,415,757,485,747,608,401,741,399,622,638,763,385,491,81,508,813,79,95,502,625,408,758,486,748,609,402,742,392,623,639,764,386,492,65,66,67,69,70,71,64,68,892,887,870,880,936,872,917,894,938,853,893,925,931,888,882,939,881,923,871,927,828,786,782,797,228,130,296,532,250,522,152,290,516,306,146,234,538,312,244,136,836,787,783,798,229,131,297,533,251,523,153,291,517,307,147,235,539,313,245,137,825,785,776,799,230,132,298,534,252,524,154,292,518,308,148,236,540,314,246,138,826,784,777,792,231,133,299,535,253,525,155,293,519,309,149,237,541,315,247,139,834,790,778,793,224,134,300,528,254,526,156,294,512,310,150,238,542,316,240,140,824,788,779,794,225,135,301,529,255,527,157,295,239,513,311,151,141,543,317,241,232,789,835,780,795,226,128,302,530,248,520,158,288,514,304,144,142,536,318,242,791,233,827,781,796,227,129,303,531,249,521,159,289,515,305,145,143,537,319,243,775,768,769,771,772,773,774,770,860,913,856,901,932,855,851,889,890,924,907,859,904,914,850,906,852,873,854,891,820,177,175,191,684,556,272,344,694,322,566,286,328,256,572,678,338,270,700,550,821,178,168,184,685,557,273,345,695,323,567,287,329,257,573,679,339,271,701,551,822,179,169,185,686,558,274,346,688,324,560,280,330,258,574,672,340,264,702,544,823,180,170,186,687,559,275,347,689,325,561,281,331,259,575,673,341,265,703,545,816,181,171,187,680,552,276,348,690,326,562,282,332,260,568,674,342,266,696,546,817,182,172,188,681,553,277,349,691,327,563,283,675,333,261,569,547,343,267,697,676,183,818,173,189,682,554,278,350,692,320,564,284,334,262,570,548,336,268,698,176,677,819,174,190,683,555,279,351,693,321,565,285,335,263,571,549,337,269,699,160,161,162,164,165,166,167,163,905,863,921,876,861,920,874,897,843,898,857,928,934,864,875,858,915,862,933,926,805,216,194,210,358,459,714,604,380,582,469,708,588,724,475,364,598,730,374,453,806,217,195,211,359,460,715,605,382,583,470,709,589,725,476,365,599,731,375,454,807,218,196,212,352,461,716,606,377,576,471,710,590,726,477,366,592,732,368,455,801,219,197,213,353,462,717,607,376,577,464,711,591,727,478,367,593,733,369,448,800,220,198,214,354,463,718,600,378,578,465,704,584,720,479,360,594,734,370,449,802,221,199,215,355,456,719,601,381,579,466,705,361,585,721,472,450,595,735,371,362,222,803,192,208,356,457,712,602,383,580,467,706,586,722,473,451,596,728,372,223,363,804,193,209,357,458,713,603,379,581,468,707,587,723,474,452,597,729,373,207,200,201,203,204,205,206,202,935,916,866,869,878,865,910,903,902,895,886,885,867,879,911,922,912,877,908,937,831,662,652,668,21,420,100,58,5,36,442,106,42,122,436,27,52,116,11,426,832,663,653,669,22,421,101,59,6,37,443,107,43,123,437,28,53,117,12,427,833,656,654,670,23,422,102,60,7,38,444,108,44,124,438,29,54,118,13,428,829,657,655,671,16,423,103,61,1,39,445,109,45,125,439,30,55,119,14,429,839,658,648,664,17,416,96,62,0,32,446,110,46,126,432,31,48,112,15,430,838,659,649,665,18,417,97,63,2,33,447,111,24,47,127,433,431,49,113,8,25,660,830,650,666,19,418,98,56,3,34,440,104,40,120,434,424,50,114,9,661,26,837,651,667,20,419,99,57,4,35,441,105,41,121,435,425,51,115,10,645,646,647,641,642,643,644,640,900,847,842,909,845,896,929,918,883,884,899,849,841,846,868,848,930,844,840,919 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 941 = 1 + 5*188, 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 = {176} 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, 188): MacNeish's product over GF(4) x GF(47); 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 19:45:27 · history