Equation 677 Database

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Magma fb691132fd4b…

magma fb691132fd4b
Size
707
Isomorphism class hash
fb691132fd4bb3a14386a1cc858aeca4b4a7dec07de62c3e9f65462a70dff4cd
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
2026-10-06 19:54:27
Display reorder
198,203,199,200,201,202,706,144,147,145,146,149,148,150,155,151,152,153,154,1,5,0,2,3,4,113,112,108,109,110,111,65,64,60,61,62,63,182,181,183,184,185,180,20,19,21,22,23,18,299,298,294,295,296,297,289,293,288,290,291,292,304,305,301,302,303,300,420,419,421,416,417,418,486,485,487,483,484,482,315,317,316,320,318,319,430,429,428,432,433,431,466,465,464,468,469,467,572,570,571,575,573,574,542,544,543,546,547,545,448,447,446,451,449,450,328,327,329,330,331,332,354,353,355,352,350,351,611,610,607,608,606,609,642,640,641,631,693,696,673,690,705,702,701,699,704,697,220,217,221,216,219,218,104,103,105,106,107,102,77,76,72,73,74,75,35,34,30,31,32,33,90,95,91,92,93,94,11,10,6,7,8,9,230,228,231,232,233,229,176,175,177,178,179,174,82,81,83,78,79,80,169,168,170,171,172,173,363,362,364,365,366,367,503,505,504,500,501,502,412,411,410,414,415,413,392,394,393,397,395,396,499,498,497,495,496,494,356,358,357,359,360,361,386,388,387,390,391,389,488,490,489,491,492,493,339,338,340,341,342,343,346,345,344,347,348,349,623,617,625,618,616,624,636,630,637,622,695,703,675,665,689,688,686,672,687,674,165,162,166,167,164,163,160,159,161,156,157,158,128,127,129,130,131,126,121,120,122,123,124,125,135,134,136,137,132,133,37,36,38,39,40,41,241,240,242,243,244,245,246,251,247,248,249,250,269,268,265,264,266,267,101,100,96,97,98,99,383,385,384,382,380,381,518,520,519,521,522,523,509,511,510,508,506,507,535,534,533,531,532,530,564,565,566,567,568,569,538,537,536,541,539,540,563,562,561,558,559,560,407,409,408,404,405,406,333,335,334,554,336,337,517,516,515,512,513,514,612,644,614,645,621,646,613,615,619,620,685,700,668,667,679,694,676,680,681,677,88,85,89,84,87,86,235,234,236,237,238,239,222,227,223,224,225,226,284,282,285,286,287,283,274,273,275,271,270,272,205,204,206,207,208,209,213,212,214,215,210,211,26,25,27,28,29,24,17,16,12,13,14,15,281,280,277,276,278,279,378,377,379,374,375,376,594,595,596,598,599,597,368,370,369,373,371,372,324,326,325,323,321,322,604,603,605,601,600,602,314,313,312,311,309,310,582,583,584,586,587,585,593,592,591,590,589,588,399,398,400,401,402,403,578,576,577,579,580,581,651,647,643,639,649,650,648,653,638,654,691,698,666,664,684,692,678,682,683,671,55,58,56,57,54,59,192,197,193,194,195,196,48,53,49,50,51,52,263,262,259,258,260,261,44,43,45,46,47,42,143,142,138,139,140,141,119,118,114,115,116,117,191,190,186,187,188,189,255,254,256,257,253,252,69,68,70,71,66,67,525,524,526,527,528,529,458,460,459,461,462,463,475,474,473,471,472,470,443,445,444,442,440,441,434,436,435,439,437,438,307,308,306,557,555,556,549,548,550,553,551,552,425,427,426,422,423,424,452,454,453,457,455,456,481,480,479,476,477,478,629,633,628,652,626,632,627,634,635,655,660,670,656,657,661,669,663,658,662,659 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#92768bb2ce71adf5f3645437d2daad1854a25afcd5bf6e7bdc519de5c37f97ae, M = {42, 43, 44, 45, 46, 47, 140} 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 2026-10-06 19:54:28 · history