Equation 677 Database

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Magma da4ceef751c7…

magma da4ceef751c7
Size
925
Isomorphism class hash
da4ceef751c73229f8c72cb651c16268182ccef62e091ca987a47c9c6f702738
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 924) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 10:22:22
Display reorder
920,921,924,923,922,564,789,489,543,471,496,788,533,502,469,791,570,479,548,522,792,790,512,577,540,565,779,487,544,472,497,778,534,503,470,781,571,480,549,523,793,780,513,576,537,566,771,488,545,473,498,770,535,504,464,782,572,481,550,524,794,772,514,578,536,567,765,486,546,474,526,764,528,505,525,783,573,482,551,527,795,773,515,579,559,561,766,485,558,516,492,762,529,506,465,784,574,483,552,518,796,774,517,580,557,560,767,507,556,475,493,763,530,508,466,785,575,797,484,553,519,555,775,509,581,798,768,562,490,541,476,494,761,531,500,467,786,569,499,554,520,538,776,510,582,769,799,563,491,542,477,495,760,532,501,468,787,568,478,547,521,539,777,511,583,595,632,609,610,611,612,613,633,863,869,870,902,871,872,866,890,862,867,864,886,861,868,865,893,585,739,356,349,280,256,741,338,264,304,738,257,284,292,331,740,753,320,271,311,584,731,357,354,351,251,742,353,265,305,724,350,285,293,352,732,754,321,272,312,586,726,358,343,279,339,743,342,263,341,725,260,340,294,332,733,755,322,273,313,587,727,359,344,323,252,744,333,262,306,723,261,286,295,326,734,756,325,274,324,588,728,360,345,278,253,745,334,314,307,721,259,287,296,327,735,757,316,275,315,589,729,361,346,277,297,746,335,267,301,722,276,736,299,300,328,308,758,317,298,737,730,590,362,347,288,254,747,336,268,302,720,258,289,290,329,309,759,318,269,749,750,591,355,348,282,255,751,337,266,303,748,281,283,291,330,310,752,319,270,592,608,605,621,622,623,607,606,880,876,897,882,875,891,873,896,881,874,903,879,898,878,877,899,73,650,44,66,27,58,641,457,84,33,667,52,7,3,444,679,659,97,18,28,74,669,45,67,20,59,668,458,85,34,671,53,8,4,445,672,670,98,19,29,75,651,46,68,21,60,640,459,86,35,661,54,9,2,446,673,660,99,17,30,90,653,88,89,22,61,652,460,91,36,662,55,10,1,447,674,654,92,15,87,79,646,47,69,23,62,645,461,80,37,663,78,77,76,448,675,655,93,16,31,70,647,48,63,24,56,643,462,81,38,664,49,676,11,0,449,32,656,94,14,677,648,71,42,64,25,57,644,463,82,41,665,50,12,39,450,40,657,95,13,649,678,72,43,65,26,454,642,456,83,453,666,51,6,5,455,452,658,96,451,593,638,626,636,624,637,625,639,851,841,844,900,852,895,846,894,840,842,843,860,889,845,887,883,196,836,204,223,166,245,814,231,150,128,806,215,142,135,186,802,824,239,160,122,197,837,205,224,167,246,815,232,151,129,807,216,140,136,187,803,825,240,161,123,198,838,206,225,168,247,816,233,152,127,808,217,141,137,188,801,826,241,162,124,199,839,207,226,169,248,817,234,153,126,809,218,139,138,189,800,827,242,163,125,200,832,210,219,117,249,830,227,155,208,829,211,154,209,190,828,831,235,156,118,193,833,201,220,191,250,820,228,147,131,819,212,818,146,145,192,119,821,236,157,810,834,194,202,221,164,243,812,229,148,132,811,213,143,133,184,120,822,237,158,835,804,195,203,222,165,244,813,230,149,130,805,214,144,134,185,121,823,238,159,594,629,616,631,627,628,615,630,847,849,858,854,848,853,859,857,892,888,885,901,856,855,850,884,114,701,102,394,108,440,703,180,372,597,713,402,415,391,171,704,702,382,428,366,112,692,103,395,109,441,694,181,373,596,714,403,416,392,172,705,693,383,429,367,113,685,101,396,110,442,695,182,374,598,715,404,417,385,173,706,686,384,430,368,376,683,375,397,111,443,696,183,378,599,716,405,418,386,174,707,687,379,431,377,432,684,100,398,105,436,697,176,433,600,717,406,419,387,175,708,688,434,435,369,116,682,420,399,106,437,698,177,422,601,718,407,709,424,388,421,363,689,423,425,710,680,410,408,400,409,438,699,178,370,602,719,412,413,389,411,364,690,380,426,681,711,115,104,393,107,439,700,179,371,603,712,401,414,390,170,365,691,381,427,604,635,617,618,620,619,614,634,904,906,912,918,907,910,914,908,916,909,915,905,917,911,913,919 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 925 = 5 + 5*184, 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 = {168, 174, 177, 181, 186} 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, 184): MacNeish's product over GF(8) x GF(23); GF(8) = F_2[x]/(x^3 + 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: 85.

last edited by qawbecrdtey at 2026-10-06 10:22:24 · history