Equation 677 Database

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Magma 4665218fb505…

magma 4665218fb505
Size
925
Isomorphism class hash
4665218fb5056c5e0a4fdb4f704b6672d91009b738c6e777f600bed15dbaa6a0
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 03:49:15
Display reorder
920,924,923,921,922,721,74,152,206,58,687,470,86,102,40,691,66,33,96,709,254,266,49,298,699,722,67,153,207,59,688,471,89,103,87,692,88,34,90,710,255,267,50,299,700,723,68,154,208,60,686,464,80,104,39,693,61,35,91,711,256,268,51,300,701,724,69,155,209,53,685,465,81,97,257,694,258,36,259,712,260,261,52,293,702,717,70,148,202,54,713,466,82,98,44,714,62,37,92,716,250,262,45,294,715,718,71,149,203,55,703,467,83,99,42,704,63,251,38,93,706,705,263,46,295,252,72,719,150,204,56,695,468,84,100,43,696,64,31,94,707,697,264,47,296,73,253,720,151,205,57,689,469,85,101,41,690,65,32,95,708,698,265,48,297,595,629,610,611,607,608,609,630,869,885,842,847,848,891,844,851,843,896,858,845,888,887,862,877,672,554,503,582,569,669,550,540,486,591,670,492,516,562,671,506,475,522,534,668,673,555,496,583,568,651,551,541,479,584,660,493,517,563,661,507,495,523,535,640,674,556,497,577,570,653,544,542,480,585,654,494,518,564,662,508,476,524,529,652,675,557,498,576,571,646,545,543,481,586,655,487,519,565,663,509,477,525,528,645,676,558,499,578,572,647,546,536,482,587,656,488,513,566,664,510,478,526,530,643,677,559,500,579,573,648,547,537,483,588,657,489,511,512,567,665,644,472,527,531,504,553,678,501,580,574,649,548,538,484,589,658,490,514,561,666,642,473,521,532,552,505,679,502,581,575,650,549,539,485,590,659,491,515,560,667,641,474,520,533,592,605,613,631,632,633,606,612,881,900,871,874,899,870,873,879,883,893,880,878,872,882,903,884,734,156,143,186,454,744,127,78,269,459,726,14,173,5,682,289,121,198,136,756,735,157,144,187,455,745,128,79,270,460,727,15,174,6,683,290,122,199,137,757,736,158,145,188,448,746,129,1,271,461,728,12,175,7,681,291,123,200,138,758,737,159,146,189,449,747,130,0,272,462,729,10,176,8,680,292,124,201,139,759,750,160,147,193,450,751,192,190,273,463,749,11,177,9,748,285,191,194,140,752,740,161,181,183,451,741,131,75,274,456,739,178,286,182,2,738,753,179,195,180,287,162,732,141,184,452,742,133,76,275,457,731,132,171,3,730,754,125,196,134,163,288,733,142,185,453,743,126,77,276,458,725,13,172,4,684,755,120,197,135,593,637,623,639,618,636,622,638,890,868,867,846,859,889,852,886,840,841,861,854,895,850,894,875,800,232,225,327,105,817,114,308,24,284,809,170,315,210,839,242,447,17,249,827,828,234,317,320,106,830,115,301,25,277,829,316,319,233,832,235,440,18,318,831,818,226,219,321,107,820,217,302,26,278,819,164,309,218,833,236,441,216,243,821,810,227,220,322,108,812,116,303,27,279,811,165,310,214,834,237,442,19,244,822,804,228,221,323,109,813,117,304,28,280,805,166,311,215,835,238,443,20,245,823,802,229,222,324,110,814,118,305,29,281,806,167,239,312,213,836,824,444,21,246,240,230,803,223,325,111,815,119,306,30,282,807,168,313,211,837,825,445,22,247,231,241,801,224,326,112,816,113,307,23,283,808,169,314,212,838,826,446,16,248,594,627,616,624,625,626,615,628,892,860,857,863,849,865,855,864,853,898,901,897,902,866,856,876,799,376,360,600,390,761,439,347,328,340,771,336,400,369,791,413,426,378,354,780,792,377,361,601,429,781,432,348,329,427,782,335,430,428,784,414,431,379,355,783,793,371,362,602,391,772,433,349,370,416,773,415,401,418,785,419,420,380,417,774,794,372,363,603,392,765,434,350,330,341,766,334,402,364,786,408,421,381,356,775,795,373,358,597,393,763,435,351,331,342,767,333,403,365,787,409,422,382,357,776,796,374,406,596,394,764,436,352,332,343,768,404,410,407,366,788,777,423,383,405,411,375,797,359,598,397,762,437,345,395,344,769,337,398,367,789,778,424,384,396,387,412,798,386,599,389,760,438,346,385,339,770,338,399,368,790,779,425,388,353,604,635,617,620,621,619,614,634,916,912,904,910,913,905,908,915,918,907,917,909,906,914,911,919 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, 174, 176, 183, 185} 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 03:49:16 · history