Equation 677 Database

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Magma 26b832ddd85c…

magma 26b832ddd85c
Size
707
Isomorphism class hash
26b832ddd85cec391b4264189459dfa6edc4774403751a0ed864844246334d2b
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 16:53:38
Display reorder
602,603,604,605,601,600,706,574,599,562,590,581,548,586,270,80,89,94,65,279,568,59,76,536,66,544,575,77,594,563,591,576,549,587,271,81,84,95,60,280,569,54,540,537,67,570,72,595,559,592,577,550,582,272,82,85,90,61,281,564,55,541,538,68,571,73,596,558,593,578,551,583,273,83,86,91,62,276,565,56,542,539,69,572,74,597,560,588,579,547,584,274,78,87,92,63,277,566,57,543,534,70,573,75,598,561,589,580,546,585,275,79,88,93,64,278,567,58,545,535,71,552,555,556,557,553,554,626,627,631,629,628,630,700,699,703,705,701,702,704,658,655,659,654,653,656,657,99,45,14,255,129,170,526,455,479,431,335,503,514,419,472,122,241,147,358,100,123,46,15,256,130,171,527,450,474,426,330,498,515,414,473,359,242,148,101,124,47,16,257,131,172,522,451,475,427,331,499,510,415,468,354,243,149,96,125,42,17,252,126,173,523,452,476,428,332,500,511,416,469,355,244,144,97,120,43,12,253,127,168,524,453,477,429,333,501,512,417,470,356,245,145,98,121,44,13,254,128,169,525,454,478,430,334,502,513,418,471,357,240,146,154,150,151,152,153,155,677,675,673,674,666,676,639,652,635,633,632,634,637,679,684,683,680,682,681,678,53,298,466,174,316,232,352,508,323,413,18,425,263,521,132,103,158,117,166,48,104,299,467,175,317,233,353,509,318,408,19,420,258,516,133,167,159,118,49,105,294,462,176,312,228,348,504,319,409,20,421,259,517,134,162,160,119,50,106,295,463,177,313,229,349,505,320,410,21,422,260,518,135,163,161,114,51,107,296,464,178,314,230,350,506,321,411,22,423,261,519,136,164,156,115,52,102,297,465,179,315,231,351,507,322,412,23,424,262,520,137,165,157,116,287,283,284,285,286,282,665,662,661,660,668,671,649,640,646,647,644,642,651,691,687,697,693,689,686,695,196,484,442,394,362,400,406,383,371,497,235,449,532,389,326,216,266,247,189,197,217,485,443,395,363,401,407,378,366,492,236,445,533,384,327,190,267,248,192,218,480,439,390,364,396,402,379,367,493,237,444,528,385,328,191,268,249,193,219,481,438,391,365,397,403,380,368,494,238,446,529,386,329,186,269,250,194,220,482,440,392,360,398,404,381,369,495,239,447,530,387,324,187,264,251,195,221,483,441,393,361,399,405,382,370,496,234,448,531,388,325,188,265,246,212,214,215,210,211,213,663,664,667,670,669,672,641,645,643,636,648,638,650,696,698,685,688,690,692,694,345,290,225,202,308,143,34,4,184,26,300,337,6,36,209,377,432,456,113,346,373,291,226,203,309,138,35,5,185,27,301,338,7,37,204,108,433,457,347,372,292,227,198,310,139,30,1,180,28,302,339,8,38,205,109,434,458,342,374,293,222,199,311,140,31,0,181,29,303,340,9,39,206,110,435,459,343,375,288,223,200,306,141,32,2,182,24,304,341,10,40,207,111,436,460,344,376,289,224,201,307,142,33,3,183,25,305,336,11,41,208,112,437,461,488,490,491,486,487,489,617,622,621,623,624,625,612,611,610,606,620,607,609,608,615,614,616,613,618,619 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#ab7663272fb322647e3a6f8af752cc36283f2dfca26817d870d65fdaf95a91e5, M = {16, 37, 57, 77, 97, 117, 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 2026-10-06 16:53:39 · history