Equation 677 Database

← all  ·  ← by size  ·  ← size 945

Magma 6f87e3dc842d…

magma 6f87e3dc842d
Size
945
Isomorphism class hash
6f87e3dc842d141836ded17a5674aa9681e071942bad938411e279faf786b37f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 944) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 17:48:00
Display reorder
52,74,63,49,39,53,75,64,50,40,54,68,65,51,41,55,69,66,44,42,56,70,67,45,43,57,71,60,46,36,58,72,61,47,37,59,73,62,48,38,942,940,943,941,944,509,559,557,556,558,644,579,571,584,586,575,581,642,565,577,508,513,512,504,510,679,664,663,665,660,580,572,585,587,576,582,641,564,578,573,588,583,566,574,643,554,553,555,500,511,124,165,174,140,157,478,76,142,125,181,164,83,133,483,481,480,482,0,149,119,166,175,141,158,479,77,143,126,182,159,84,134,487,485,484,486,1,150,120,167,176,136,153,477,78,144,127,177,160,85,135,491,489,488,490,2,151,121,168,171,137,154,145,475,79,86,128,178,161,146,131,495,493,492,494,3,152,122,169,172,138,155,476,80,87,129,179,162,132,147,499,497,496,498,4,148,123,170,173,139,156,474,81,82,130,180,163,467,468,469,471,472,473,466,470,911,914,912,913,910,881,886,885,888,887,884,889,882,883,880,936,935,937,938,939,192,270,379,254,317,387,307,334,420,436,198,257,368,25,187,263,22,92,403,193,271,380,249,318,382,302,330,416,432,199,258,369,26,188,264,17,93,404,194,266,375,250,313,383,303,612,633,638,591,598,620,563,589,599,561,505,546,514,525,542,597,610,625,608,613,634,658,647,649,655,645,590,600,562,567,547,515,526,543,524,531,545,530,534,549,677,666,668,674,661,183,265,18,88,399,189,267,376,251,314,384,304,331,417,433,195,259,184,365,27,400,260,19,89,185,190,268,377,252,315,385,305,332,418,434,196,255,366,23,401,261,20,90,191,186,269,378,253,316,386,306,333,419,435,197,256,367,24,402,262,21,91,32,33,34,28,29,30,31,35,904,893,894,898,902,896,899,903,895,901,890,897,891,892,900,876,875,873,874,872,622,632,607,637,611,605,568,630,594,628,540,519,502,523,533,560,592,596,569,621,631,651,657,653,650,646,629,593,627,619,520,503,522,532,501,516,521,506,541,548,670,676,672,669,662,405,206,393,359,233,12,243,319,5,204,242,108,370,411,297,427,325,286,102,406,207,394,360,234,13,244,320,6,205,237,109,371,412,298,428,326,287,103,407,208,395,361,235,14,245,321,7,200,238,110,372,413,299,429,327,288,104,408,209,396,362,236,322,15,246,111,8,201,239,323,373,414,300,430,328,289,105,409,210,397,363,231,16,247,112,9,202,240,374,324,415,301,431,329,290,106,410,211,398,364,232,11,248,107,10,203,241,97,98,99,101,94,95,96,100,871,866,867,878,860,924,929,921,922,926,931,934,933,932,930,916,918,919,917,915,338,440,221,118,275,465,462,461,463,464,228,351,391,311,425,357,284,295,346,339,441,222,113,276,444,279,341,381,443,229,352,392,312,426,358,285,296,347,340,442,223,114,277,445,278,614,623,639,595,616,626,609,635,617,603,529,538,535,550,517,570,601,640,602,615,624,659,648,654,656,652,636,618,604,606,539,536,551,518,507,527,552,528,537,544,678,667,673,675,671,421,353,280,291,342,335,437,224,115,272,449,447,446,448,450,230,348,422,388,308,343,354,281,292,423,336,438,225,116,273,455,452,451,453,454,226,349,389,309,344,355,282,293,337,424,439,220,117,274,460,457,456,458,459,227,350,390,310,345,356,283,294,219,212,213,215,216,217,218,214,909,906,905,907,908,863,869,868,864,862,865,879,861,877,870,928,925,927,923,920,720,741,697,787,707,730,832,808,824,816,683,797,755,769,766,717,744,695,800,721,742,698,788,708,731,833,809,825,817,684,798,756,770,767,718,745,688,801,722,743,699,789,709,732,834,810,826,818,685,799,757,771,760,719,746,689,802,723,736,700,790,710,733,835,811,827,819,686,792,758,772,761,712,747,690,803,724,737,701,791,711,734,836,812,828,820,687,793,759,773,762,713,748,691,804,725,738,702,784,704,735,837,813,829,821,681,794,763,752,774,805,714,749,692,764,726,739,703,785,705,728,838,814,830,822,680,795,753,775,806,715,750,693,727,765,740,696,786,706,729,839,815,831,823,682,796,754,768,807,716,751,694,777,778,779,781,782,783,776,780,847,853,843,845,842,855,858,856,857,859,844,850,851,852,849,848,841,846,854,840 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 945 = 45 + 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#6da6d029496de4ba04f593353aa3ac64edf7f49c62b836ac7c04d9b960787c66, M = the submagma generated by {0, 6} (45 elements) 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: 105.

last edited by qawbecrdtey at 2026-10-07 17:48:01 · history