Equation 677 Database

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Magma f5b5ab8e5d1f…

magma f5b5ab8e5d1f
Size
707
Isomorphism class hash
f5b5ab8e5d1ffa9864cd63bdb0c0a78043327250da17ed921d5965191c6e9511
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
2026-10-08 23:56:16
Display reorder
603,604,605,601,600,602,706,594,248,546,264,584,554,536,545,561,570,236,279,576,568,590,243,286,274,262,595,588,246,548,265,582,553,535,543,562,571,234,280,577,569,244,287,263,275,596,589,247,547,266,583,552,534,544,563,572,235,281,578,567,245,285,261,273,542,557,559,573,239,276,579,564,593,597,251,550,267,587,539,271,259,283,240,537,555,541,558,574,237,277,580,566,591,598,249,551,268,585,272,260,241,284,556,540,538,560,575,238,278,581,565,592,599,250,549,269,586,242,270,258,282,252,253,257,255,256,254,675,677,676,672,673,674,627,628,631,632,630,629,626,701,699,703,704,702,700,705,126,533,519,510,206,182,114,508,498,229,523,496,165,227,140,392,425,202,427,127,138,531,520,511,204,180,115,509,499,230,524,497,166,225,391,423,426,203,128,139,532,521,512,205,181,116,507,500,228,522,495,167,226,390,424,428,201,505,185,501,232,526,492,162,224,143,129,530,516,513,209,117,199,429,422,395,118,183,506,502,233,527,494,163,222,141,130,529,517,514,207,200,430,393,421,184,504,119,503,231,525,493,164,223,142,131,528,518,515,208,394,198,431,420,159,160,158,156,157,161,646,640,638,647,639,645,697,695,698,692,693,696,694,655,663,661,651,662,654,664,35,361,73,96,7,487,468,42,58,366,69,110,358,86,377,467,452,459,479,33,375,360,74,97,8,488,469,43,59,368,70,108,359,84,465,451,477,460,34,376,362,72,98,6,486,470,44,57,367,71,109,357,85,466,450,478,461,45,490,55,370,66,113,354,89,374,32,363,76,99,10,471,456,476,455,464,472,491,46,56,371,67,111,356,87,373,30,364,77,100,11,457,474,462,453,489,47,473,54,369,68,112,355,88,372,31,365,75,101,9,463,458,475,454,483,484,482,480,481,485,649,636,644,643,637,650,679,682,680,678,684,683,681,666,668,670,669,665,671,667,351,447,90,440,347,413,415,437,62,21,400,383,37,14,51,80,384,403,107,350,52,448,91,439,345,411,414,435,60,22,401,381,38,12,78,386,105,402,348,53,449,92,438,346,412,416,436,61,23,399,382,36,13,79,385,106,404,434,410,65,18,396,380,40,17,48,349,444,93,443,344,417,405,104,388,83,418,409,433,63,19,398,379,41,15,49,352,445,94,441,343,406,102,81,389,408,432,419,64,20,397,378,39,16,50,353,446,95,442,342,82,407,103,387,291,292,290,288,289,293,633,641,648,642,635,634,691,689,685,688,687,686,690,658,659,660,657,652,653,656,316,171,194,154,332,294,3,305,327,308,28,219,132,213,318,175,120,341,144,317,320,172,192,155,331,295,4,303,328,307,29,220,133,214,176,121,145,339,315,319,173,193,153,330,296,5,304,329,306,27,221,134,215,174,122,146,340,302,297,325,311,25,216,135,210,322,312,168,197,151,335,1,338,147,123,178,0,298,301,324,309,26,217,136,211,323,314,169,195,152,333,337,148,179,124,299,300,2,326,310,24,218,137,212,321,313,170,196,150,334,177,336,149,125,190,191,186,187,188,189,617,621,608,610,611,622,613,607,623,616,618,606,615,620,624,619,625,614,609,612 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#a8026a02368cc98eace7a76910bb242dec082e21ec6371f1fc7226b87fb07666, M = {10, 31, 51, 64, 85, 105, 128} 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 2026-10-08 23:56:17 · history