Equation 677 Database

← all  ·  ← by size  ·  ← size 765

Magma 46b678738c06…

magma 46b678738c06
Size
765
Isomorphism class hash
46b678738c0678760fe69c7efd7a15cedcba44f1026721c567435c043dbc7076
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 764) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-09 06:05:05
Display reorder
220,240,60,72,258,221,241,61,73,259,222,242,54,74,260,223,243,55,75,261,216,236,56,68,262,217,237,57,69,255,218,238,58,70,256,219,239,59,71,257,696,682,693,687,697,263,362,153,7,378,396,22,185,343,330,204,200,302,426,14,264,363,154,8,379,397,23,186,344,331,205,201,303,427,15,265,364,149,9,380,398,500,548,599,591,558,556,584,622,497,571,603,539,494,607,612,498,549,600,332,206,202,304,428,16,266,358,150,10,375,393,19,182,340,333,207,203,305,429,17,267,359,151,11,376,394,20,183,341,197,334,208,18,306,430,198,360,268,152,12,377,395,21,184,342,335,209,13,307,431,361,199,269,540,495,606,611,499,547,598,592,557,496,583,621,555,490,664,553,554,665,671,670,761,759,757,755,756,758,760,705,706,718,717,716,715,720,719,714,643,646,638,648,645,566,537,644,642,536,576,574,562,532,559,551,615,552,448,336,244,146,326,372,138,278,270,224,136,214,188,404,190,449,337,245,147,327,373,139,279,271,225,137,215,189,405,191,450,338,246,148,328,374,534,577,572,561,533,560,550,616,493,627,593,565,538,590,605,535,575,573,226,132,210,187,406,6,451,339,247,143,329,371,272,140,275,211,227,133,273,457,453,452,458,455,248,144,454,456,141,276,212,228,134,470,274,462,463,472,468,249,145,467,469,142,277,213,229,135,481,485,489,480,484,488,678,679,739,735,741,736,738,737,740,681,709,698,689,699,695,692,683,763,45,105,250,122,127,4,231,437,192,286,121,421,90,433,170,46,106,251,123,128,5,232,438,193,287,119,422,91,434,171,47,107,252,124,129,0,233,439,194,288,120,423,92,435,172,41,101,253,125,130,1,234,440,195,289,118,424,93,436,173,42,102,254,126,131,2,235,441,196,290,117,425,523,624,544,508,528,631,628,629,491,563,634,630,620,633,632,545,524,625,419,103,43,465,460,461,3,230,471,464,466,459,174,94,432,104,420,44,640,636,637,492,564,647,639,641,635,546,525,623,594,595,669,596,597,668,674,675,749,747,745,754,752,748,746,722,724,713,723,721,688,725,727,726,519,516,505,586,610,502,601,582,522,511,619,531,510,503,543,520,513,506,315,387,24,353,296,88,63,413,112,52,30,165,80,76,37,316,388,25,354,297,89,64,414,113,53,31,166,81,77,38,317,389,26,355,298,84,65,415,114,48,32,167,82,78,39,318,390,27,356,299,85,66,416,115,49,33,168,83,79,40,319,391,28,357,300,86,116,67,417,169,50,34,529,514,517,507,587,609,501,602,581,521,512,618,542,509,504,515,530,518,36,314,392,29,352,301,87,62,418,164,51,35,478,482,486,479,483,487,676,677,734,733,732,729,731,730,728,680,694,684,690,712,686,685,691,764,109,176,320,280,410,445,474,294,402,369,385,350,99,312,159,110,177,321,281,411,446,473,295,403,370,386,351,100,313,160,111,178,322,282,412,447,663,653,614,656,657,655,526,654,650,651,660,588,652,659,661,662,579,658,365,381,345,95,308,155,161,179,323,283,407,442,476,291,399,366,382,346,96,309,156,162,180,324,284,408,443,477,292,400,347,367,383,157,97,310,348,181,163,325,285,409,444,475,293,401,368,384,158,98,311,175,349,108,589,578,617,626,649,580,613,604,608,541,527,585,567,568,667,569,570,666,672,673,750,762,743,753,744,742,751,703,711,707,708,710,701,702,700,704 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 765 = 45 + 5*144, 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 = the submagma generated by {3, 5} (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, 144): MacNeish's product over GF(16) x GF(9); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-09 06:05:06 · history