Equation 677 Database

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Magma 0de83df95a02…

magma 0de83df95a02
Size
707
Isomorphism class hash
0de83df95a021a14fbc04472cece819c73679f30d1001142fc2b7133a9d572e1
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 12:09:17
Display reorder
184,183,185,180,181,182,706,294,295,296,297,298,299,62,64,63,60,61,65,149,148,144,145,146,147,137,136,132,133,134,135,173,172,168,169,170,171,288,289,290,291,292,293,102,107,103,104,105,106,245,244,240,241,242,243,122,121,123,124,125,120,304,305,301,302,303,300,309,311,310,307,306,308,573,575,574,570,572,571,444,446,445,448,449,447,459,461,460,458,456,457,430,429,431,427,428,426,513,515,514,512,510,511,399,401,400,398,396,397,419,418,417,416,414,415,579,581,580,578,577,576,381,383,382,380,378,379,629,630,634,633,631,632,638,637,639,635,701,680,693,703,702,689,700,694,705,704,80,79,81,82,83,78,157,159,158,161,156,160,253,252,257,254,255,256,220,219,221,216,217,218,267,266,268,269,265,264,53,52,48,49,50,51,10,9,11,6,7,8,258,259,260,261,262,263,101,100,96,97,98,99,225,224,226,227,222,223,481,480,482,484,485,483,562,561,563,560,559,558,535,536,534,538,539,537,501,503,502,500,498,499,468,470,469,471,472,473,325,324,326,327,328,329,321,323,322,320,318,319,339,341,340,336,337,338,548,546,547,550,551,549,540,541,542,543,544,545,627,614,612,628,613,618,616,617,623,622,699,696,695,687,673,666,679,665,686,685,67,66,68,69,70,71,209,205,204,207,208,206,117,116,118,119,114,115,72,77,73,74,75,76,236,235,237,238,239,234,113,112,108,109,110,111,276,277,278,279,280,281,56,55,57,58,59,54,153,152,154,155,150,151,165,164,166,167,162,163,490,489,491,487,488,486,566,564,565,567,568,569,532,531,533,530,529,528,522,523,524,525,526,527,375,377,376,372,373,374,497,496,495,493,494,492,587,586,585,583,584,582,557,556,555,554,553,552,423,425,424,422,420,421,335,334,333,331,332,330,626,642,624,641,625,640,615,621,620,619,691,692,688,683,667,671,675,670,677,698,285,284,286,287,283,282,90,92,91,94,95,93,32,31,33,34,35,30,273,272,274,275,271,270,213,212,214,215,210,211,41,40,36,37,38,39,47,46,42,43,44,45,24,29,25,26,27,28,85,84,86,87,88,89,233,232,228,229,230,231,358,357,359,355,356,354,602,600,601,603,604,605,367,366,368,371,369,370,349,348,350,351,352,353,363,365,364,360,361,362,437,436,435,433,434,432,591,593,592,590,589,588,594,595,596,598,599,597,346,345,347,342,343,344,477,479,478,476,474,475,647,644,648,645,646,643,651,653,650,654,697,678,682,681,672,668,676,674,684,690,2,0,3,4,5,1,20,22,21,18,19,23,194,193,195,196,197,192,17,16,12,13,14,15,127,126,128,129,130,131,249,248,250,251,247,246,141,140,142,143,138,139,198,203,199,200,201,202,191,190,186,187,188,189,178,177,179,174,175,176,505,504,506,508,509,507,465,467,466,463,464,462,316,315,317,314,312,313,394,393,395,390,391,392,517,518,516,519,520,521,406,405,407,402,403,404,454,453,455,450,451,452,443,442,441,440,438,439,385,384,386,387,388,389,413,412,411,409,410,408,609,649,611,608,606,610,652,607,636,655,663,660,662,664,658,657,659,656,661,669 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#20e9cec11ce1b4ef3a4be2ce0eb77a027f26009c155c08499f343b203c8ba1b3, M = {60, 61, 62, 63, 64, 65, 144} 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 12:09:18 · history