Equation 677 Database

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Magma 6bf0812733fd…

magma 6bf0812733fd
Size
925
Isomorphism class hash
6bf0812733fdee577f911a7c454c7d815f882f464979dd3fcbd312b8f7c4824e
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
2026-10-08 13:57:44
Display reorder
920,921,923,922,924,721,756,743,741,319,451,570,252,636,213,356,173,392,182,415,479,279,603,309,539,757,758,669,668,320,444,571,245,637,214,349,174,393,183,416,480,280,604,310,540,722,723,670,666,321,445,572,246,638,215,350,175,394,184,417,481,281,605,311,541,767,768,742,762,322,446,573,247,639,216,351,176,395,185,418,482,282,606,312,542,724,725,671,665,323,447,574,248,632,217,352,177,396,186,419,483,283,607,313,543,733,734,672,664,324,448,575,249,633,218,353,178,536,389,187,412,476,276,600,314,661,719,673,662,317,449,568,250,634,315,354,179,537,390,180,413,477,277,601,316,660,720,674,663,318,450,569,251,635,212,355,172,538,391,181,414,478,278,602,308,667,822,813,809,810,811,812,821,890,868,863,862,896,902,910,881,872,914,906,898,885,913,873,877,658,650,704,736,254,609,286,577,227,400,189,497,358,407,546,226,453,484,422,327,659,651,705,770,255,610,287,578,228,401,190,498,359,408,547,219,454,485,423,328,761,760,765,764,256,611,288,579,169,402,191,499,360,409,548,220,455,486,424,329,655,654,706,696,257,612,289,580,170,403,192,500,361,410,549,221,456,487,425,330,656,652,707,697,258,613,290,581,171,404,193,501,362,411,550,222,457,488,426,331,740,653,752,751,259,614,291,582,168,397,194,502,332,363,405,551,223,458,489,427,657,727,729,698,253,615,284,583,167,398,195,503,325,357,406,544,224,459,490,420,701,699,703,702,492,608,285,576,491,399,188,496,326,493,494,545,225,452,495,421,700,806,807,820,818,819,805,808,907,903,886,918,869,874,865,859,919,864,894,878,882,899,891,887,646,643,711,718,622,434,558,266,93,526,370,235,466,509,590,81,339,297,202,72,645,644,712,732,623,435,559,267,94,527,371,236,467,510,591,82,340,298,203,73,730,713,731,714,616,428,552,260,87,520,364,229,460,511,584,83,333,299,196,74,739,737,753,754,617,429,553,261,88,521,365,230,461,504,585,84,334,292,197,75,648,640,708,715,618,430,554,262,89,522,366,231,462,505,586,85,335,293,198,76,649,641,709,716,619,431,555,263,90,523,367,232,77,463,506,587,86,336,294,199,647,642,710,717,620,432,556,264,91,524,368,233,78,464,507,588,79,337,295,200,759,738,766,755,621,433,557,265,92,525,369,234,71,465,508,589,80,338,296,201,771,836,828,838,829,839,830,837,888,870,916,866,908,900,858,883,895,912,875,848,892,904,879,860,693,677,747,745,475,626,594,4,346,97,206,374,439,515,271,384,535,307,240,563,750,744,748,683,468,627,595,5,347,98,207,375,440,516,272,385,528,300,241,564,735,678,691,684,469,628,596,6,348,99,208,376,441,517,273,386,529,301,242,565,769,763,749,746,470,629,597,0,341,100,209,377,442,518,274,387,530,302,243,566,695,685,687,686,471,630,598,1,342,101,210,378,443,519,275,388,531,303,244,567,728,726,688,680,472,631,599,379,343,102,211,380,560,436,512,268,381,532,304,237,694,675,689,681,473,624,592,2,344,95,204,372,561,437,513,269,382,533,305,238,692,676,690,682,474,625,593,3,345,96,205,373,562,438,514,270,383,534,306,239,679,825,814,823,827,826,815,824,909,901,849,884,893,905,880,861,915,911,876,917,889,871,897,867,778,777,776,779,42,18,114,154,8,50,146,122,64,162,138,58,34,130,106,26,783,782,781,780,43,19,115,155,9,51,147,123,65,163,139,59,35,131,107,27,786,785,784,787,44,20,116,156,10,52,148,124,66,164,140,60,36,132,108,28,790,789,788,791,45,21,117,157,11,53,149,125,67,165,141,61,37,133,109,29,794,793,792,795,46,22,118,158,12,54,150,126,68,166,142,62,38,134,110,30,798,797,796,799,39,15,111,151,13,47,143,119,23,69,159,135,55,31,127,103,802,801,800,803,40,16,112,152,14,48,144,120,24,70,160,136,56,32,128,104,774,772,773,775,41,17,113,153,7,49,145,121,25,63,161,137,57,33,129,105,804,835,817,832,833,831,816,834,841,856,845,852,844,851,840,855,857,846,853,842,847,854,843,850 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#892b5616c7779dfec415627d945de6de06210babab60b9ffd32cbcc3e1be41da, M = {168, 169, 170, 171, 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 2026-10-08 13:57:45 · history