Equation 677 Database

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Magma facbf17e61ea…

magma facbf17e61ea
Size
941
Isomorphism class hash
facbf17e61eab6ee9b267a585d2287c865d7c1ba16ae2ff068dbf40e7f19b3af
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
2026-10-06 23:47:05
Display reorder
940,309,556,10,454,635,629,819,619,460,572,20,293,550,315,26,470,566,299,4,476,310,557,11,455,636,630,826,620,461,573,21,294,551,316,27,471,567,300,5,477,311,558,12,448,637,631,821,621,462,574,22,295,544,317,28,464,560,301,6,478,304,559,13,449,638,624,822,622,463,575,23,288,545,318,29,465,561,302,7,479,305,552,14,450,639,625,823,623,456,568,16,289,546,319,30,466,562,303,1,472,306,553,15,451,632,626,824,616,457,569,17,290,467,547,312,31,473,563,296,0,468,554,307,8,452,633,627,825,617,458,570,18,291,548,313,24,474,564,297,2,555,469,308,9,453,634,628,820,618,459,571,19,292,549,314,25,475,565,298,3,612,613,614,608,609,610,611,615,882,917,888,918,913,901,875,859,883,897,908,860,873,884,939,861,874,881,935,919,95,490,409,227,39,45,831,61,233,506,393,79,484,81,387,243,500,65,403,249,88,491,410,228,32,46,832,62,234,507,394,72,485,82,388,244,501,66,404,250,89,492,411,229,33,47,833,63,235,508,395,73,486,83,389,245,502,67,405,251,90,493,412,230,34,40,828,56,236,509,396,74,487,84,390,246,503,68,406,252,91,494,413,231,35,41,839,57,237,510,397,75,480,85,391,247,496,69,407,253,92,495,414,224,36,42,838,58,238,511,398,76,240,481,86,384,254,497,70,400,241,488,93,415,225,37,43,829,59,239,504,399,77,482,87,385,255,498,71,401,489,242,94,408,226,38,44,830,60,232,505,392,78,483,80,386,248,499,64,402,54,55,48,50,51,52,53,49,876,925,840,903,856,911,930,842,914,910,926,841,855,877,869,843,929,933,868,902,352,206,779,266,421,427,836,443,260,222,789,382,192,366,795,282,208,368,773,276,353,207,780,267,422,428,816,444,261,223,790,383,193,367,796,283,209,369,774,277,354,200,781,268,423,429,817,445,262,216,791,376,194,360,797,284,210,370,775,278,355,201,782,269,416,430,818,446,263,217,784,377,195,361,798,285,211,371,768,279,356,202,783,270,417,431,812,447,256,218,785,378,196,362,799,286,212,372,769,272,357,203,776,271,418,424,813,440,257,219,786,379,287,197,363,792,273,213,373,770,280,204,358,777,264,419,425,814,441,258,220,787,380,198,364,793,274,214,374,771,205,281,359,778,265,420,426,815,442,259,221,788,381,199,365,794,275,215,375,772,436,437,438,432,433,434,435,439,906,872,871,870,858,924,931,867,854,900,865,866,907,928,896,864,857,853,938,912,739,166,680,331,112,126,808,96,325,182,690,761,172,745,696,347,188,755,674,341,740,167,681,332,113,127,809,97,326,183,691,762,173,746,697,348,189,756,675,342,741,160,682,333,114,120,810,98,327,176,692,763,174,747,698,349,190,757,676,343,742,161,683,334,115,121,811,99,320,177,693,764,175,748,699,350,191,758,677,336,743,162,684,335,116,122,800,100,321,178,694,765,168,749,700,351,184,759,678,337,736,163,685,328,117,123,835,101,322,179,695,766,344,169,750,701,338,185,752,679,345,164,737,686,329,118,124,806,102,323,180,688,767,170,751,702,339,186,753,672,165,346,738,687,330,119,125,807,103,324,181,689,760,171,744,703,340,187,754,673,109,110,111,105,106,107,108,104,904,844,927,846,863,937,932,893,852,922,891,892,909,905,898,890,862,851,894,845,130,522,706,662,601,595,801,585,668,538,728,152,516,136,722,652,532,146,712,646,131,523,707,663,602,596,803,586,669,539,729,153,517,137,723,653,533,147,713,647,132,524,708,656,603,597,804,587,670,540,730,154,518,138,724,654,534,148,714,640,133,525,709,657,604,598,837,588,671,541,731,155,519,139,725,655,535,149,715,641,134,526,710,658,605,599,827,589,664,542,732,156,512,140,726,648,528,150,716,642,135,527,711,659,606,592,805,590,665,543,733,157,649,513,141,727,643,529,151,717,650,520,128,704,660,607,593,834,591,666,536,734,158,514,142,720,644,530,144,718,521,651,129,705,661,600,594,802,584,667,537,735,159,515,143,721,645,531,145,719,578,579,580,582,583,576,577,581,879,885,916,886,889,936,920,850,880,923,848,849,934,915,899,847,921,878,895,887 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#e2e02209b152089c952baaa7fc77816bd26a47b0a80992ce8db26c94e6b3550e, M = {168} 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 2026-10-06 23:47:06 · history