Equation 677 Database

← all  ·  ← by size  ·  ← size 876

Magma 3a7c7d0e1ec6…

magma 3a7c7d0e1ec6
Size
876
Isomorphism class hash
3a7c7d0e1ec679dd7d30ac738eee28c6d361a049418148f698f85d3bca34e3e5
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
2026-10-08 19:01:07
Display reorder
872,172,334,28,234,162,245,19,8,153,267,690,173,335,29,235,691,163,246,20,9,154,268,174,336,30,236,692,21,164,247,10,142,269,175,337,31,237,693,248,165,22,11,143,257,176,338,32,238,694,249,23,12,166,144,258,167,339,177,33,239,250,24,13,145,695,259,155,340,178,34,240,251,25,1,146,696,260,341,156,179,35,241,252,26,2,147,697,261,157,342,180,36,242,253,27,3,148,698,262,343,158,168,37,243,254,15,4,149,699,263,159,344,169,38,244,255,16,5,150,700,264,160,345,170,39,233,256,17,6,151,701,265,161,346,171,40,702,703,18,7,788,813,791,817,815,816,814,704,705,14,0,152,706,266,824,820,823,818,821,819,822,735,743,745,738,858,870,855,841,857,875,873,856,874,854,539,45,677,129,181,487,587,424,309,347,634,540,46,678,130,635,182,488,588,425,310,348,528,47,679,131,636,589,183,476,426,311,349,529,48,680,132,637,477,184,590,427,312,350,530,49,681,133,638,478,578,428,185,313,351,186,50,531,682,134,479,579,429,314,639,352,187,51,532,683,135,480,580,430,315,628,353,52,188,533,684,136,481,581,431,316,629,354,189,53,534,685,137,482,582,432,317,630,355,41,190,535,686,138,483,583,433,318,631,356,191,42,536,687,139,484,584,434,319,632,357,192,43,537,688,140,485,585,435,320,633,358,193,44,538,689,141,486,586,436,717,731,718,707,713,725,734,787,799,806,798,793,809,795,778,774,751,782,756,757,771,741,748,746,739,864,867,863,833,830,849,840,848,834,842,469,294,207,303,411,672,522,567,626,117,75,470,295,208,304,76,412,673,523,568,627,118,471,283,209,305,77,524,413,674,569,616,119,472,284,210,306,66,675,414,525,570,617,120,473,285,211,307,67,676,526,571,415,618,121,416,286,474,212,308,664,527,572,619,68,122,417,287,475,213,296,665,515,573,620,69,123,288,418,463,214,297,666,516,574,621,70,124,419,289,464,215,298,667,517,575,622,71,125,290,420,465,216,299,668,518,576,623,72,126,421,291,466,217,300,669,519,577,624,73,127,422,292,467,218,301,670,520,565,625,74,128,423,293,468,219,302,671,521,566,730,709,712,716,721,724,714,792,812,802,805,808,784,786,753,770,761,759,762,767,781,740,775,777,736,862,871,860,829,852,839,847,832,853,828,438,367,101,386,602,496,194,321,547,640,55,439,368,102,387,56,603,497,195,322,548,641,440,369,103,388,57,196,591,498,323,549,642,441,370,91,389,58,499,592,197,324,550,643,442,371,92,390,59,500,198,325,593,551,644,594,359,443,93,391,501,199,326,552,60,645,595,360,444,94,392,489,200,327,541,61,646,361,596,445,95,393,490,201,328,542,62,647,597,362,446,96,394,491,202,329,543,63,648,363,598,447,97,395,492,203,330,544,64,649,599,364,448,98,396,493,204,331,545,65,650,600,365,449,99,397,494,205,332,546,54,651,601,366,437,100,385,495,206,333,726,708,732,719,728,722,710,797,800,789,794,803,783,810,752,768,763,754,765,776,772,758,747,749,779,859,868,861,826,844,843,850,835,836,831,110,277,406,513,460,372,220,82,553,610,652,111,278,407,514,653,461,373,221,83,554,611,112,279,408,502,654,222,462,374,84,555,612,113,280,409,503,655,375,450,223,85,556,613,114,281,410,504,656,376,224,86,451,557,614,452,282,115,398,505,377,225,87,558,657,615,453,270,116,399,506,378,226,88,559,658,604,271,454,104,400,507,379,227,89,560,659,605,455,272,105,401,508,380,228,90,561,660,606,273,456,106,402,509,381,229,78,562,661,607,457,274,107,403,510,382,230,79,563,662,608,458,275,108,404,511,383,231,80,564,663,609,459,276,109,405,512,384,232,81,727,733,729,715,723,711,720,801,796,790,785,804,811,807,780,755,760,766,773,769,764,737,744,750,742,869,865,866,825,851,838,846,827,845,837 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#54d57920567b129973738a4f9ba70087188034e7a635c7156940b0bb23159c34, 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 2026-10-08 19:01:08 · history