Equation 677 Database

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Magma 7e0adbb01932…

magma 7e0adbb01932
Size
707
Isomorphism class hash
7e0adbb019321494a767207a37364ae9002d47bd4568bbdf67f85a396e55d1a5
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 10:47:48
Display reorder
304,303,305,300,302,301,656,81,82,78,79,80,83,40,39,41,38,37,36,234,236,235,237,238,239,254,252,253,257,256,255,160,159,161,157,158,156,295,294,296,299,297,298,76,75,77,73,74,72,280,279,281,278,277,276,260,258,259,263,261,262,142,141,143,138,139,140,535,534,536,537,538,539,601,605,600,602,603,604,540,545,541,542,543,544,366,371,367,368,369,370,449,448,444,445,446,447,355,354,356,357,358,359,332,331,333,334,335,330,360,365,361,362,363,364,583,582,584,585,586,587,576,581,577,578,579,580,633,611,617,628,608,616,636,622,620,637,701,704,699,683,695,698,696,702,694,684,103,104,106,107,105,102,57,59,58,55,56,54,137,136,135,134,132,133,85,84,86,89,87,88,275,274,273,272,271,270,287,286,285,282,283,284,165,167,166,162,163,164,290,289,288,291,292,293,266,264,265,269,267,268,186,188,187,191,189,190,457,456,458,459,460,461,595,599,594,596,597,598,572,571,573,574,575,570,403,402,404,405,406,407,529,528,530,531,532,533,550,549,551,546,547,548,375,374,376,377,372,373,590,589,591,592,593,588,501,500,502,503,498,499,495,494,496,497,492,493,650,641,649,651,638,648,635,624,621,634,693,692,680,665,688,691,689,700,687,668,123,124,120,121,122,125,144,146,145,148,149,147,19,18,20,22,23,21,32,31,30,33,34,35,27,29,28,24,25,26,196,195,197,194,192,193,99,101,100,96,97,98,202,201,203,200,198,199,244,243,245,240,242,241,247,248,246,251,249,250,557,556,552,553,554,555,561,560,562,563,558,559,567,566,568,569,564,565,443,442,438,439,440,441,420,425,421,422,423,424,468,473,469,470,471,472,327,326,328,329,324,325,437,436,432,433,434,435,426,431,427,428,429,430,507,506,508,509,504,505,655,647,643,653,639,645,626,631,632,625,690,703,697,673,678,670,671,672,682,666,206,204,209,207,208,205,42,43,44,47,45,46,63,65,64,60,61,62,213,215,214,211,212,210,233,232,231,230,228,229,14,13,12,15,16,17,117,119,118,114,115,116,183,185,184,181,182,180,110,109,108,113,111,112,151,150,152,153,154,155,474,479,475,476,477,478,344,343,345,346,347,342,392,391,393,394,395,390,413,412,408,409,410,411,519,518,520,521,516,517,453,452,454,455,450,451,483,482,484,485,480,481,515,514,510,511,512,513,486,491,487,488,489,490,336,341,337,338,339,340,652,640,646,654,642,644,629,623,619,630,705,686,706,667,669,685,677,674,675,676,48,49,51,52,53,50,130,129,131,128,126,127,4,3,5,0,2,1,11,10,9,6,7,8,169,168,170,172,173,171,177,179,178,175,176,174,219,221,220,216,217,218,225,227,226,223,224,222,71,70,69,68,66,67,95,94,93,91,92,90,306,307,308,309,310,311,526,525,527,522,523,524,318,323,319,320,321,322,381,380,382,383,378,379,313,312,314,315,316,317,389,388,384,385,386,387,351,350,352,353,348,349,397,396,398,399,400,401,462,467,463,464,465,466,416,415,417,418,419,414,618,609,607,627,606,612,615,614,610,613,679,661,681,659,660,664,657,658,662,663 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#21508ce76d8339c8cc8a9db508194b7933fb8eb19570d11d640cb6bc14178d14, M = {24, 25, 26, 27, 28, 29, 134} 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 10:47:49 · history