Equation 677 Database

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Magma 8e060df09201…

magma 8e060df09201
Size
707
Isomorphism class hash
8e060df09201204bcecc5f5071af87e9650de1c41e855b5aab40bb6cb5aabac0
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 14:24:07
Display reorder
486,491,487,488,489,490,673,121,122,124,125,123,120,212,211,210,213,214,215,135,137,136,132,133,134,194,193,192,195,196,197,295,294,296,298,299,297,325,324,326,328,329,327,216,218,217,220,221,219,182,181,180,185,183,184,186,188,187,190,191,189,127,126,128,130,131,129,143,142,141,139,140,138,424,423,425,420,421,422,364,369,365,366,367,368,444,449,445,446,447,448,438,443,439,440,441,442,433,432,434,435,436,437,415,414,416,417,418,419,460,459,461,456,457,458,563,562,564,565,596,591,593,597,592,595,594,566,637,629,627,628,626,660,636,635,655,640,641,693,684,668,670,706,671,667,705,662,47,45,44,42,43,46,52,51,53,50,48,49,306,308,307,309,310,311,77,76,75,72,73,74,12,14,13,15,16,17,323,322,321,320,318,319,275,274,273,270,271,272,204,206,205,207,208,209,58,57,59,56,54,55,260,259,258,263,261,262,293,292,291,289,290,288,600,599,601,598,548,549,465,464,466,467,462,463,471,470,472,473,468,469,350,349,351,346,347,348,476,475,477,478,479,474,480,485,481,482,483,484,408,407,406,575,576,577,573,572,574,571,344,345,411,410,412,413,409,578,616,654,648,657,612,659,614,639,619,613,650,694,704,687,661,666,692,691,672,685,60,61,63,64,65,62,2,0,1,3,4,5,264,266,265,267,268,269,200,199,198,201,202,203,305,304,303,302,300,301,163,162,164,166,167,165,161,160,159,156,157,158,114,116,115,117,118,119,282,284,283,286,287,285,239,238,237,236,234,235,253,252,254,255,256,257,530,535,531,532,533,534,539,538,540,541,536,537,520,519,521,522,523,518,381,380,376,377,378,379,357,356,352,353,354,355,358,363,359,360,361,362,553,552,554,583,584,585,582,581,579,580,510,511,558,557,559,560,561,590,638,647,644,649,615,632,653,625,656,608,631,674,696,681,677,699,678,663,676,682,222,223,225,226,227,224,169,168,170,173,171,172,241,240,242,244,245,243,145,144,146,149,147,148,101,100,99,98,96,97,317,316,315,314,312,313,85,84,86,89,87,88,24,25,26,28,29,27,71,70,69,66,67,68,82,81,83,79,80,78,11,10,9,7,8,6,602,605,603,604,550,551,396,395,397,398,399,394,513,512,514,515,516,517,506,505,507,508,509,504,493,492,494,495,496,497,386,385,387,382,383,384,338,337,336,567,568,569,588,587,589,586,555,556,340,339,341,342,343,570,651,607,621,645,642,658,618,609,622,633,617,698,697,690,675,664,689,669,695,680,41,39,38,36,37,40,32,31,30,33,34,35,23,22,21,20,18,19,94,93,95,92,90,91,103,102,104,106,107,105,276,278,277,279,280,281,176,175,174,177,178,179,153,155,154,150,151,152,230,229,228,231,232,233,249,251,250,246,247,248,112,111,113,108,109,110,330,331,332,333,334,335,501,500,502,503,498,499,451,450,452,453,454,455,403,402,404,405,400,401,527,526,528,529,525,524,427,426,428,429,430,431,543,542,544,545,546,547,370,375,371,372,373,374,391,390,392,393,388,389,620,624,646,606,611,652,643,630,623,610,634,679,683,700,686,665,688,702,701,703 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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#21508ce76d8339c8cc8a9db508194b7933fb8eb19570d11d640cb6bc14178d14, M = {114, 115, 116, 117, 118, 119, 145} 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, 140): MacNeish's product over GF(4) x GF(5) x GF(7); GF(4) = F_2[x]/(x^2 + 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: 101.

last edited by qawbecrdtey at 2026-10-07 14:24:08 · history