Equation 677 Database

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Magma 996e0077a0ae…

magma 996e0077a0ae
Size
925
Isomorphism class hash
996e0077a0ae33602187aa1a01f28a0fa9ec9ddf8f756b6b12aa0bc432f3f32e
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 08:52:11
Display reorder
921,923,920,922,924,43,751,362,74,742,50,11,219,39,722,56,38,29,752,67,82,207,7,195,732,41,744,355,75,743,51,12,220,31,720,57,23,30,753,68,83,208,8,196,733,42,745,356,76,736,52,13,221,32,734,58,24,25,754,69,84,209,6,197,735,40,746,357,77,737,53,14,222,33,726,59,22,26,755,70,85,210,5,198,727,199,747,358,78,738,201,200,223,34,724,60,20,27,756,71,86,203,54,202,728,46,748,359,79,739,47,15,224,35,725,61,21,87,72,757,73,729,204,10,192,88,749,44,360,80,740,48,16,225,36,723,64,19,63,758,65,730,205,62,193,750,89,45,361,81,741,49,17,226,37,721,55,18,28,759,66,731,206,9,194,118,619,605,606,607,608,609,622,878,844,871,843,876,858,868,881,864,860,875,866,856,872,841,863,467,786,443,456,798,365,423,403,463,762,434,387,413,778,481,371,378,398,393,769,468,787,444,454,799,366,424,404,464,761,435,389,414,779,482,388,379,399,394,770,469,791,445,452,792,367,425,405,458,788,436,386,415,790,483,380,381,400,395,789,470,781,446,453,793,368,426,406,459,760,437,384,416,780,477,374,363,401,390,771,471,782,447,451,794,369,427,407,460,772,442,385,441,774,476,375,438,440,439,773,474,783,448,472,795,370,428,408,473,765,431,383,373,417,775,478,766,429,396,430,419,784,465,449,457,796,418,421,409,461,763,432,382,420,776,479,767,376,402,391,785,372,466,450,455,797,364,422,411,462,764,433,410,412,777,480,768,377,397,392,475,611,610,630,628,629,612,613,903,853,902,896,855,883,887,847,889,895,894,882,852,897,888,854,159,805,103,126,804,148,105,95,186,813,128,178,113,823,136,265,127,214,171,835,160,806,97,1,802,149,106,96,187,814,129,179,114,824,137,266,119,215,172,836,161,807,98,2,803,150,107,91,188,815,130,180,115,825,138,267,120,216,173,837,162,808,99,3,801,151,108,92,189,816,131,181,116,826,139,268,121,217,174,838,163,809,100,4,800,152,109,93,190,817,132,182,117,827,140,269,122,218,175,839,167,829,101,164,828,153,110,165,191,830,133,183,262,166,831,141,832,123,211,168,263,819,157,102,154,818,156,111,94,184,820,134,176,155,821,142,833,124,212,169,811,264,158,145,143,810,147,104,144,185,812,135,177,112,822,146,834,125,213,170,90,637,621,636,618,639,620,638,859,880,861,867,873,862,845,840,846,879,870,877,869,865,874,857,292,667,303,339,679,291,294,314,280,640,228,327,293,657,290,352,247,231,259,650,271,671,304,340,672,241,295,315,282,668,281,328,283,670,236,353,248,229,260,669,272,661,305,341,673,251,296,316,276,658,249,329,284,660,250,354,252,230,261,659,273,662,306,346,674,242,297,317,345,644,342,330,285,652,344,347,243,343,254,651,274,663,307,335,675,238,333,318,332,645,0,334,286,653,237,348,244,331,255,646,275,664,308,336,676,321,322,323,277,643,319,324,349,287,654,320,647,245,234,256,350,665,270,311,337,677,239,298,312,278,641,227,325,288,655,309,648,310,232,257,666,351,300,302,338,678,240,301,313,279,642,299,326,289,656,235,649,246,233,258,253,624,614,626,627,623,615,625,899,900,851,849,850,890,884,892,885,891,842,848,901,893,886,898,525,694,600,573,693,542,503,502,517,714,534,504,594,705,581,486,553,558,565,692,526,695,601,574,686,543,500,518,520,715,535,519,595,706,580,487,554,559,566,685,527,696,602,575,687,544,501,496,512,716,536,505,589,707,582,488,555,560,564,683,546,697,603,576,688,547,545,495,528,717,529,506,588,708,583,489,548,561,571,684,521,698,597,577,689,538,499,537,513,718,530,507,590,709,584,490,549,562,570,682,522,699,596,578,690,539,497,494,514,719,531,508,491,591,710,585,680,550,563,568,484,700,523,598,579,691,540,498,492,515,712,532,509,592,711,586,681,551,556,569,703,485,524,599,572,702,541,510,493,516,713,533,511,593,704,587,701,552,557,567,604,635,617,631,632,633,616,634,907,918,905,908,915,911,917,904,912,913,910,916,906,914,909,919 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 = {169, 170, 177, 180, 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 2026-10-08 08:52:12 · history