Equation 677 Database

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Magma 69bc67fbd5d0…

magma 69bc67fbd5d0
Size
707
Isomorphism class hash
69bc67fbd5d07c0381bbf5cd2dd2235b5512e760b9de953c1c96b52e6a130fcd
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 12:52:09
Display reorder
376,375,371,372,373,374,664,97,96,99,100,101,98,34,33,35,32,30,31,210,212,211,215,213,214,217,216,218,220,221,219,3,5,4,1,0,2,106,105,107,103,104,102,248,247,246,249,250,251,224,223,222,227,225,226,83,82,81,79,80,78,74,73,72,75,76,77,229,228,230,232,233,231,395,400,396,397,398,399,486,485,487,488,489,490,498,497,499,500,501,502,479,484,480,481,482,483,422,421,423,424,419,420,519,518,520,521,516,517,495,494,496,491,492,493,563,562,564,565,596,591,593,597,592,595,594,566,637,616,643,606,642,638,619,636,609,617,646,705,704,670,706,671,675,669,672,662,47,46,43,44,42,45,22,21,23,20,18,19,85,84,86,87,88,89,192,194,193,195,196,197,166,165,167,163,164,162,40,39,41,37,38,36,154,153,155,152,150,151,91,90,92,94,95,93,24,26,25,29,27,28,147,149,148,145,146,144,208,207,209,205,206,204,602,605,603,604,537,538,412,411,407,408,409,410,529,528,530,525,526,527,535,534,536,531,532,533,459,458,460,455,456,457,430,429,425,426,427,428,550,549,551,581,582,580,584,583,585,586,552,553,351,350,352,349,348,567,633,624,635,628,613,618,610,640,641,608,645,701,696,689,686,676,691,688,687,667,119,118,115,116,114,117,11,10,9,6,7,8,108,110,109,113,111,112,320,319,318,323,321,322,315,317,316,312,313,314,308,307,306,311,309,310,270,272,271,274,275,273,296,295,294,299,297,298,127,126,128,129,130,131,191,190,189,186,187,188,133,132,134,136,137,135,385,384,386,387,388,383,465,464,466,461,462,463,559,558,560,561,557,556,507,506,508,503,504,505,449,454,450,451,452,453,392,391,393,394,389,390,547,546,548,578,579,577,576,575,573,574,544,545,512,511,513,514,515,568,659,632,622,658,621,655,657,620,607,647,651,703,699,668,700,698,690,665,697,666,283,282,285,286,287,284,174,176,175,178,179,177,140,139,138,142,143,141,260,259,258,263,261,262,302,301,300,305,303,304,160,159,161,157,158,156,328,327,329,326,324,325,201,203,202,198,199,200,12,14,13,17,15,16,172,171,173,170,168,169,254,253,252,257,255,256,599,598,600,601,510,509,432,431,433,434,435,436,469,468,470,471,472,467,444,443,445,446,447,448,442,441,437,438,439,440,358,357,353,354,355,356,523,522,524,569,570,571,588,587,589,590,554,555,540,539,541,542,543,572,649,629,648,656,653,634,625,623,630,612,660,702,695,692,694,693,674,663,661,677,50,49,52,53,51,48,55,54,56,59,57,58,278,277,276,280,281,279,64,63,65,61,62,60,245,244,243,242,240,241,66,68,67,69,70,71,124,123,125,122,120,121,264,266,265,267,268,269,182,181,180,184,185,183,289,288,290,293,291,292,237,239,238,234,235,236,404,403,405,406,401,402,473,478,474,475,476,477,334,333,335,331,330,332,338,337,339,340,341,336,342,347,343,344,345,346,360,359,361,362,363,364,414,413,415,416,417,418,369,368,370,365,366,367,379,378,380,381,382,377,627,654,639,644,611,650,615,652,614,631,626,673,681,682,679,678,683,685,684,680 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#53d992532d406ee1a16d046074f6b11dc06c8f5c6df8c27dc9277719dd794878, M = {96, 97, 98, 99, 100, 101, 139} 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 12:52:10 · history