Equation 677 Database

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Magma 4483854f0351…

magma 4483854f0351
Size
925
Isomorphism class hash
4483854f0351e7d12dab6ea68c4602eeeb9db83c02457723fcf446eec29d5064
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 15:02:11
Display reorder
923,920,922,924,921,568,501,531,714,681,586,513,492,522,567,690,572,706,477,570,569,504,699,571,542,485,544,532,715,682,587,514,493,545,543,691,573,707,476,556,547,505,700,560,546,486,495,535,716,683,588,515,534,523,494,692,574,708,533,557,548,506,701,561,536,487,496,526,717,684,589,516,488,525,472,693,575,709,524,558,549,507,702,562,537,482,497,527,718,685,590,517,489,518,480,694,576,710,481,559,550,508,703,563,538,483,498,528,719,686,591,510,490,519,474,695,577,551,711,478,553,539,509,696,564,552,499,484,529,712,687,585,511,491,520,475,688,578,704,479,554,540,502,697,565,500,582,580,530,713,680,584,512,581,521,473,689,583,705,579,555,541,503,698,566,592,622,609,605,606,607,608,623,875,877,890,871,879,891,892,874,878,885,873,872,876,903,880,881,26,169,457,753,738,75,76,14,87,451,741,212,739,25,39,24,185,740,204,74,27,170,458,754,730,68,77,16,88,452,742,213,731,17,40,15,186,732,205,55,28,171,459,755,724,69,78,8,89,453,743,214,725,18,38,4,187,733,206,56,29,172,460,756,722,70,79,9,90,454,744,215,726,19,36,5,188,734,207,57,30,173,461,757,723,71,80,10,91,455,745,208,727,20,37,6,189,735,200,58,31,174,462,758,721,72,81,11,92,448,746,209,7,728,21,35,59,190,736,201,3,175,32,463,759,720,73,82,12,93,449,747,210,729,22,34,0,191,737,202,168,2,33,456,752,748,84,85,13,86,450,751,211,749,23,83,1,184,750,203,593,611,612,624,625,626,610,613,898,868,843,851,848,897,854,869,901,840,886,846,841,899,857,893,223,296,323,815,825,269,272,339,444,252,803,270,807,331,253,288,280,837,268,271,224,297,324,816,826,231,273,340,445,245,801,238,808,332,254,289,281,838,221,261,225,298,325,817,827,232,274,341,446,246,800,239,809,333,255,290,282,839,222,262,226,299,326,830,831,233,275,342,447,247,828,240,829,334,256,291,283,832,220,263,227,300,327,820,821,234,276,343,440,248,818,241,819,335,257,292,284,833,218,264,228,301,328,812,822,235,277,344,441,249,810,242,293,811,336,258,265,285,834,219,294,302,229,329,813,823,236,278,345,442,250,804,243,805,337,259,266,286,835,217,303,295,230,330,814,824,237,279,346,443,251,802,244,806,338,260,267,287,836,216,594,639,618,637,627,638,628,636,889,860,894,865,867,858,864,900,859,884,863,902,861,862,866,882,110,468,140,657,667,199,183,117,118,54,650,67,640,167,100,133,159,679,41,151,103,469,143,670,671,192,176,142,119,101,669,60,668,160,102,126,152,672,141,144,104,470,134,660,661,193,177,111,120,48,659,61,658,161,94,127,153,673,47,145,105,471,135,652,662,194,178,112,121,49,651,62,644,162,95,128,154,674,45,146,106,464,136,653,663,195,179,113,122,50,646,63,645,163,96,129,155,675,46,147,107,465,137,654,664,196,180,114,123,51,647,64,130,643,164,97,148,156,676,44,131,466,108,138,655,665,197,181,115,124,52,648,65,641,165,98,149,157,677,42,467,132,109,139,656,666,198,182,116,125,53,649,66,642,166,99,150,158,678,43,595,631,616,633,629,630,615,632,855,844,856,883,887,888,870,849,842,853,847,845,852,850,895,896,364,411,318,775,785,398,308,360,353,371,763,437,767,390,378,383,316,797,424,597,365,412,361,776,786,399,309,362,354,372,761,438,768,391,379,384,317,798,425,596,363,413,319,777,787,400,310,355,347,373,760,439,769,392,380,385,311,799,426,598,427,414,320,790,791,401,304,356,348,428,788,432,789,393,429,430,312,792,431,599,417,419,416,780,781,402,305,357,349,418,778,433,779,394,374,386,415,793,420,600,367,408,404,772,782,407,403,405,350,406,770,434,387,771,395,375,601,313,794,421,381,409,368,321,773,783,396,306,358,351,369,764,435,765,388,376,602,314,795,422,410,382,366,322,774,784,397,307,359,352,370,762,436,766,389,377,603,315,796,423,604,635,617,619,620,621,614,634,908,913,915,909,912,906,914,907,918,916,911,910,904,905,917,919 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 = {170, 174, 175, 182, 184} 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 15:02:20 · history