Equation 677 Database

← all  ·  ← by size  ·  ← size 876

Magma 917041d5cc29…

magma 917041d5cc29
Size
876
Isomorphism class hash
917041d5cc29aed782ab6f1e940482ca5594d378271d92d641f0a478af51ca4b
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 826 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 04:10:24
Display reorder
857,20,80,702,250,444,22,446,82,690,238,23,447,83,691,239,24,448,70,692,240,25,435,71,693,241,26,436,72,694,242,27,437,73,695,243,14,438,74,696,244,15,439,75,697,245,16,440,76,698,246,17,441,77,699,247,18,442,78,700,248,19,443,79,701,249,21,445,81,689,251,335,121,508,367,601,322,122,509,368,602,323,123,510,369,603,324,124,511,370,604,325,125,512,371,590,326,112,513,372,591,327,113,514,373,592,328,114,515,374,593,329,115,516,375,594,330,116,517,376,595,331,117,518,377,596,332,118,519,378,597,333,119,505,364,598,334,120,506,365,599,791,808,794,817,800,807,796,507,366,600,706,703,704,705,819,820,821,822,823,824,818,713,722,718,714,864,830,853,854,855,842,852,829,850,831,102,312,184,2,126,104,128,314,186,4,105,129,315,187,5,106,130,316,188,6,107,131,317,189,7,108,132,318,190,8,109,133,319,191,9,110,134,320,192,10,111,135,321,193,11,98,136,308,194,12,99,137,309,195,13,100,138,310,182,0,101,139,311,183,1,103,127,313,185,3,400,163,88,230,555,401,164,89,231,556,402,165,90,232,557,403,166,91,233,558,404,167,92,234,559,405,154,93,235,560,406,155,94,236,561,393,156,95,237,548,394,157,96,224,549,395,158,97,225,550,396,159,84,226,551,397,160,85,227,552,398,161,86,228,553,399,162,87,229,554,739,740,753,743,737,757,742,795,799,814,803,804,805,806,752,747,748,749,750,782,751,710,721,717,709,870,851,875,856,827,825,838,826,834,828,34,498,577,359,453,36,455,500,579,361,37,456,501,580,362,38,457,502,581,363,39,458,503,582,350,40,459,504,583,351,41,460,491,584,352,28,461,492,585,353,29,462,493,586,354,30,449,494,587,355,31,450,495,588,356,32,451,496,589,357,33,452,497,576,358,35,454,499,578,360,640,422,219,272,686,641,423,220,273,687,642,424,221,274,688,643,425,222,275,675,644,426,223,276,676,645,427,210,277,677,646,428,211,278,678,633,429,212,279,679,634,430,213,266,680,635,431,214,267,681,636,432,215,268,682,637,433,216,269,683,638,434,217,270,684,639,421,218,271,685,738,760,762,775,755,778,759,798,801,816,810,811,812,813,771,763,764,765,766,767,768,712,769,770,711,865,871,872,843,840,835,844,841,839,846,337,482,544,205,671,339,673,484,546,207,340,674,485,547,208,341,661,486,534,209,342,662,487,535,196,343,663,488,536,197,344,664,489,537,198,345,665,490,538,199,346,666,477,539,200,347,667,478,540,201,348,668,479,541,202,349,669,480,542,203,336,670,481,543,204,338,672,483,545,206,629,259,301,68,43,630,260,302,69,44,631,261,303,56,45,632,262,304,57,46,619,263,305,58,47,620,264,306,59,48,621,265,307,60,49,622,252,294,61,50,623,253,295,62,51,624,254,296,63,52,625,255,297,64,53,626,256,298,65,54,627,257,299,66,55,628,258,300,67,42,754,779,761,773,744,777,745,802,793,792,788,785,786,787,729,730,731,732,733,781,735,736,719,715,734,874,873,867,862,866,859,860,863,868,861,420,291,575,617,148,408,150,293,563,605,409,151,280,564,606,410,152,281,565,607,411,153,282,566,608,412,140,283,567,609,413,141,284,568,610,414,142,285,569,611,415,143,286,570,612,416,144,287,571,613,417,145,288,572,614,418,146,289,573,615,419,147,290,574,616,407,149,292,562,618,388,520,171,648,476,389,521,172,649,463,390,522,173,650,464,391,523,174,651,465,392,524,175,652,466,379,525,176,653,467,380,526,177,654,468,381,527,178,655,469,382,528,179,656,470,383,529,180,657,471,384,530,181,658,472,385,531,168,659,473,386,532,169,660,474,387,533,170,647,475,758,741,746,774,776,756,772,797,815,809,783,789,790,784,726,727,728,725,724,780,723,707,720,716,708,858,869,845,847,832,836,848,837,833,849 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 876 = 1 + 5*175, 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#635f59cbacdd2f28581899083344f4b3b4fefe48e856a88a52a7d40e6c05cdd5, M = {165} 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, 175): MacNeish's product over GF(25) x GF(7); GF(25) = F_5[x]/(x^2 + 2); 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: 51.

last edited by qawbecrdtey at 2026-10-07 04:10:25 · history