Equation 677 Database

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Magma 4ead4c6cf043…

magma 4ead4c6cf043
Size
909
Isomorphism class hash
4ead4c6cf04375bcf9f14b4d41f43cc6e0f1a021684f518c6fb2859cda2ce91c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 908) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 20:37:47
Display reorder
803,804,805,806,807,801,800,802,908,366,400,176,318,160,414,368,288,193,209,223,398,382,174,304,190,352,384,302,367,401,177,319,161,415,369,289,194,210,216,399,383,175,305,191,353,385,303,360,402,178,312,162,408,370,290,195,211,217,392,376,168,306,184,354,386,296,361,403,179,313,163,409,371,291,196,212,218,393,377,169,307,185,355,387,297,362,404,180,314,164,410,372,292,197,213,219,394,378,170,308,186,356,388,298,363,405,181,315,165,411,373,293,198,214,220,309,395,379,171,299,187,357,389,310,406,364,182,316,166,412,374,294,199,215,221,396,380,172,300,188,358,390,407,311,365,183,317,167,413,375,295,192,208,222,397,381,173,301,189,359,391,206,207,200,202,203,204,205,201,858,862,863,882,876,832,830,840,841,847,852,849,848,851,850,888,887,891,892,884,134,335,4,113,26,321,156,111,463,479,465,351,150,20,127,10,140,337,97,135,328,5,114,27,322,157,104,456,472,466,344,151,21,120,11,141,338,98,128,329,6,115,28,323,158,105,457,473,467,345,144,22,121,12,142,339,99,129,330,7,116,29,324,159,106,458,474,468,346,145,23,122,13,143,340,100,130,331,1,117,30,325,152,107,459,475,469,347,146,16,123,14,136,341,101,131,332,0,118,31,326,153,108,460,476,470,124,348,147,17,102,15,137,342,125,333,132,2,119,24,327,154,109,461,477,471,349,148,18,103,8,138,343,334,126,133,3,112,25,320,155,110,462,478,464,350,149,19,96,9,139,336,448,449,450,452,453,454,455,451,868,880,859,875,871,881,879,870,866,874,861,867,869,873,860,835,836,828,839,846,514,563,517,545,637,602,620,629,531,611,573,520,578,599,511,559,540,512,588,515,564,518,546,638,603,621,630,532,612,574,522,579,592,510,552,541,508,589,509,565,519,547,639,604,622,631,533,613,575,523,580,593,500,553,542,483,590,495,566,504,548,632,605,623,624,534,614,568,524,581,594,501,554,543,484,591,496,567,505,549,633,606,616,625,535,615,569,525,582,595,502,555,536,485,584,497,561,506,550,634,607,617,626,528,608,570,503,526,583,596,585,556,537,482,499,560,494,507,551,635,600,618,627,529,609,571,527,576,597,586,557,538,480,562,498,513,516,544,636,601,619,628,530,610,572,521,577,598,587,558,539,481,490,491,492,486,487,488,489,493,856,855,857,854,853,900,895,898,905,894,907,896,904,899,897,901,893,902,906,903,79,226,33,271,63,232,81,287,430,446,432,242,95,49,257,47,65,248,273,72,227,34,264,56,233,82,280,431,447,433,243,88,50,258,40,66,249,274,73,228,35,265,57,234,83,281,424,440,434,244,89,51,259,41,67,250,275,74,229,36,266,58,235,84,282,425,441,435,245,90,52,260,42,68,251,276,75,230,37,267,59,236,85,283,426,442,436,246,91,53,261,43,69,252,277,76,231,38,268,60,237,86,284,427,443,437,262,247,92,54,278,44,70,253,263,224,77,39,269,61,238,87,285,428,444,438,240,93,55,279,45,71,254,225,256,78,32,270,62,239,80,286,429,445,439,241,94,48,272,46,64,255,423,416,417,419,420,421,422,418,864,878,877,865,872,845,844,837,829,834,842,831,838,833,843,883,886,889,885,890,698,766,654,734,655,772,683,750,719,709,703,781,677,669,740,648,693,787,756,699,767,643,735,656,773,684,751,720,710,704,782,670,662,741,649,686,788,757,700,768,644,736,657,774,685,752,721,711,705,783,671,663,742,650,687,789,758,694,769,645,737,658,775,678,753,722,712,706,784,672,664,743,651,688,790,759,695,770,642,738,659,776,679,754,723,713,707,785,673,665,744,652,689,791,760,696,771,640,739,660,777,680,755,724,714,708,745,786,674,666,761,653,690,792,746,764,697,641,733,661,778,681,748,717,715,701,779,675,667,762,646,691,793,765,747,797,795,798,796,799,682,749,718,716,702,780,676,668,763,647,692,794,732,725,726,728,729,730,731,727,813,818,808,826,820,816,819,823,815,827,811,812,822,824,809,814,821,810,825,817 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 909 = 9 + 5*180, 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 = {11, 31, 51, 71, 91, 111, 132, 152, 179} 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, 180): MacNeish's product over GF(4) x GF(9) x GF(5); GF(4) = F_2[x]/(x^2 + x + 1), GF(9) = F_3[x]/(x^2 + 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: 101.

last edited by qawbecrdtey at 2026-10-07 20:37:48 · history