Equation 677 Database

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Magma 6d79f5f5ad5d…

magma 6d79f5f5ad5d
Size
925
Isomorphism class hash
6d79f5f5ad5da3d93ffb1d3a66661424e9bf967343f1264ddb50763603ddb3af
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
2026-10-07 23:25:02
Display reorder
923,922,921,920,924,281,563,190,78,761,760,759,754,350,612,587,53,327,45,383,214,69,409,461,448,451,564,191,79,662,661,660,659,351,613,588,450,328,449,452,215,70,402,454,453,282,565,192,80,663,653,652,651,352,614,589,54,329,46,384,216,71,403,455,442,283,566,193,81,664,654,650,642,353,615,590,55,330,47,385,217,72,404,456,443,284,567,194,82,665,655,648,643,354,608,591,56,323,48,379,210,73,405,457,444,278,560,187,75,666,656,649,641,347,609,584,50,211,324,49,380,445,74,406,458,212,561,279,188,76,667,657,647,640,348,610,585,51,325,43,381,446,67,407,459,562,213,280,189,77,668,658,646,644,349,611,586,52,326,44,382,447,68,408,460,645,818,809,805,806,807,808,819,911,877,908,848,866,905,855,917,845,858,874,918,885,891,846,916,488,500,289,167,674,673,693,683,414,303,473,524,508,546,481,310,174,296,516,466,489,501,290,168,675,669,694,684,415,304,474,525,509,547,482,311,175,297,517,467,490,502,291,169,676,670,695,685,416,305,475,526,510,548,483,312,176,298,518,468,491,503,292,170,677,671,696,686,417,306,476,527,511,549,484,313,177,299,519,469,495,496,285,163,678,672,697,687,410,493,494,520,504,550,477,314,178,492,512,462,485,497,286,164,763,762,755,764,411,300,470,521,307,505,551,478,463,171,293,513,308,498,486,287,165,689,688,691,690,412,301,471,522,506,544,479,464,172,294,514,499,309,487,288,166,681,679,692,682,413,302,472,523,507,545,480,465,173,295,515,680,812,811,822,821,820,813,810,870,886,893,887,895,899,868,898,903,871,896,894,869,892,849,897,270,179,268,628,747,701,716,708,139,123,104,269,129,159,147,552,394,109,372,434,271,180,117,629,750,702,717,709,140,124,105,261,130,160,148,553,395,110,373,435,272,181,118,630,753,698,758,756,141,122,103,262,131,161,149,554,396,111,374,436,273,182,116,631,771,765,766,757,142,120,102,263,132,162,150,555,397,112,375,437,274,183,114,624,735,710,712,711,153,121,151,264,133,155,154,556,398,152,376,438,275,184,115,625,738,704,713,705,143,119,101,265,557,134,156,144,439,399,106,377,558,185,276,113,626,741,699,714,706,137,135,100,266,136,157,145,440,400,107,378,186,559,277,126,627,744,700,715,707,138,127,125,267,128,158,146,441,401,108,371,703,838,823,836,825,839,824,837,862,902,863,913,872,854,852,865,861,904,851,853,850,890,884,881,638,255,606,247,768,769,770,767,37,236,346,583,428,322,366,538,66,209,29,226,639,256,607,248,730,734,733,718,38,237,339,576,429,315,367,539,25,203,30,227,632,257,600,249,732,736,737,731,39,238,340,577,430,316,368,540,26,204,31,228,633,258,601,250,725,739,740,724,40,239,341,578,431,317,369,541,27,205,32,229,634,259,602,251,726,742,743,719,41,240,342,579,432,318,370,542,24,206,33,230,635,260,603,252,727,745,746,720,42,241,343,580,543,433,319,363,231,23,207,34,536,253,636,604,245,728,748,749,721,35,244,344,581,426,320,364,232,242,243,28,254,537,637,605,246,729,751,752,722,36,235,345,582,427,321,365,234,65,208,233,723,826,814,829,827,828,815,830,883,843,876,919,915,864,910,907,873,901,889,880,857,860,844,914,88,220,594,8,776,777,778,779,420,618,19,197,571,389,1,531,334,98,358,64,89,221,595,9,781,780,782,783,421,619,20,198,572,390,0,532,335,99,359,57,91,222,596,10,785,784,786,787,422,620,21,199,573,391,90,533,336,92,360,58,83,223,597,12,789,788,790,791,423,621,22,200,574,392,11,534,337,93,361,59,84,224,598,14,793,792,794,795,424,622,15,201,575,393,13,535,338,94,362,60,85,225,599,5,797,796,798,799,425,623,16,202,528,568,386,4,61,331,95,355,529,218,86,592,6,801,800,802,803,418,616,17,195,569,387,2,62,332,96,356,219,530,87,593,7,772,773,774,775,419,617,18,196,570,388,3,63,333,97,357,804,835,817,832,833,831,816,834,912,888,841,842,847,859,909,856,882,900,906,840,878,867,875,879 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, 170, 171, 172, 188} 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 2026-10-07 23:25:03 · history