Equation 677 Database

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Magma cd8aa3d443e5…

magma cd8aa3d443e5
Size
925
Isomorphism class hash
cd8aa3d443e583d715e8637256f133c650608a74ac50aa7ad482606951912781
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 11:20:16
Display reorder
924,922,920,923,921,80,245,285,745,64,757,332,272,727,247,256,244,462,723,88,65,735,248,264,246,81,56,286,746,43,758,333,273,728,237,257,42,463,721,89,66,736,249,265,57,74,50,287,747,44,759,326,274,729,238,258,40,464,720,82,67,737,250,266,58,75,51,280,751,45,752,327,275,749,239,259,41,457,748,83,68,750,251,267,59,76,52,281,741,46,753,328,276,739,240,260,39,458,738,84,69,740,252,268,60,77,53,282,742,47,754,329,277,731,241,261,37,70,459,730,85,61,732,253,269,71,54,78,283,743,48,755,330,278,725,242,262,38,460,724,86,62,733,254,270,55,73,79,284,744,49,756,331,279,726,243,263,72,461,722,87,63,734,255,271,594,627,609,605,606,607,608,628,853,844,894,848,846,842,895,849,845,886,887,852,851,883,847,882,555,501,470,641,516,660,522,545,672,480,540,531,563,671,506,583,651,570,489,476,556,502,471,661,517,663,521,546,673,481,538,532,564,664,507,584,662,569,490,477,557,503,472,652,518,654,523,547,674,482,539,533,565,665,508,578,653,571,491,478,558,496,465,645,519,655,524,548,675,483,537,534,566,666,509,577,646,572,492,479,560,497,466,643,520,656,525,549,676,484,559,535,567,667,512,579,647,573,493,511,552,498,467,644,513,657,526,550,677,485,543,536,580,568,668,510,473,648,574,494,581,499,553,468,642,514,658,527,551,678,486,541,530,562,669,504,474,649,575,495,500,582,554,469,640,515,659,528,544,679,487,542,529,561,670,505,475,650,576,488,595,611,612,630,631,629,610,613,902,863,888,870,867,889,861,900,869,868,890,866,862,865,864,896,20,32,105,778,324,762,294,455,770,316,2,115,338,786,28,235,798,94,11,304,21,30,106,779,325,763,296,456,771,317,295,116,339,787,29,236,799,95,12,297,22,107,108,790,318,788,288,449,789,310,1,109,340,791,23,229,792,96,13,298,15,36,100,780,319,764,289,450,772,311,97,110,341,781,98,230,793,99,14,299,16,34,101,774,320,765,290,451,773,312,6,111,334,782,24,231,794,90,7,300,17,35,102,775,321,766,291,452,767,313,4,112,232,335,783,25,301,795,91,8,233,33,18,103,776,322,760,292,453,768,314,5,113,336,784,26,302,796,92,9,31,234,19,104,777,323,761,293,454,769,315,3,114,337,785,27,303,797,93,10,0,636,632,638,633,639,618,637,850,857,855,860,885,840,897,856,899,843,854,859,841,884,858,898,352,388,438,831,423,832,440,441,829,436,376,439,590,828,362,305,830,437,410,377,424,389,425,821,428,833,429,442,819,347,426,399,591,818,363,306,820,348,427,378,356,390,366,822,417,834,430,443,811,345,370,400,592,810,365,307,812,364,411,379,357,391,367,823,418,835,431,444,805,346,371,401,586,804,358,308,813,349,412,380,414,392,368,824,419,836,432,445,806,344,372,402,585,802,359,309,814,413,416,415,354,393,369,825,420,837,433,446,807,404,373,406,403,587,803,360,381,815,405,407,394,396,355,395,826,421,838,434,447,808,343,374,397,588,801,361,382,816,350,408,387,383,353,385,827,422,839,435,448,809,342,375,398,589,800,384,386,817,351,409,593,622,616,624,625,626,615,623,903,892,878,877,872,874,880,875,871,876,891,893,901,873,879,881,125,170,195,695,223,694,150,603,714,211,141,180,169,705,168,203,696,187,160,167,126,171,196,687,224,686,151,597,715,212,142,181,161,706,133,204,697,188,153,122,124,172,197,688,225,684,152,596,716,213,143,182,162,707,134,205,698,189,154,123,144,173,198,689,226,685,146,598,717,214,145,183,163,708,135,206,699,190,155,121,129,174,199,690,227,683,147,599,718,215,137,184,164,709,136,207,700,191,156,119,128,175,200,691,228,681,148,600,719,216,138,185,208,165,710,130,120,701,192,157,209,176,217,201,692,221,682,149,601,712,220,139,219,218,711,131,118,702,193,158,178,202,127,194,693,222,680,177,602,713,210,140,179,166,704,132,117,703,186,159,604,635,617,619,620,621,614,634,918,916,910,904,906,909,915,912,908,905,907,914,917,911,913,919 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 = {171, 173, 175, 180, 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 11:20:17 · history