Equation 677 Database

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Magma ac934fc8b26a…

magma ac934fc8b26a
Size
707
Isomorphism class hash
ac934fc8b26a9d77e6cfaadec61782f77bd34a004bb97a9f4a28348ecc69d324
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 00:49:09
Display reorder
181,180,182,183,184,185,706,295,299,294,296,297,298,53,50,48,49,52,51,24,29,25,26,27,28,107,106,102,103,104,105,72,77,73,74,75,76,288,289,290,291,292,293,9,8,10,11,6,7,245,244,240,241,242,243,33,32,34,35,30,31,304,305,301,302,303,300,397,396,398,400,401,399,575,574,573,572,571,570,514,513,515,512,510,511,469,468,470,471,472,473,372,374,373,377,375,376,351,353,352,350,348,349,485,484,483,481,482,480,411,413,412,410,408,409,580,579,581,577,576,578,333,335,334,331,332,330,629,630,634,633,631,632,638,637,639,635,701,680,693,703,702,689,700,694,705,704,173,172,168,169,170,171,87,84,88,89,86,85,253,252,257,254,255,256,163,162,164,165,166,167,264,265,266,267,268,269,211,210,212,213,214,215,202,201,203,198,199,200,262,261,263,259,258,260,222,227,223,224,225,226,93,92,94,95,90,91,309,311,310,307,306,308,561,563,562,559,558,560,536,534,535,537,538,539,507,509,508,506,504,505,393,395,394,392,390,391,491,490,489,487,488,486,316,315,317,312,313,314,423,425,424,422,420,421,550,549,551,547,546,548,542,540,541,543,544,545,627,614,612,628,613,618,616,617,623,622,699,696,695,687,673,666,679,665,686,685,123,122,124,125,120,121,136,133,137,132,135,134,41,40,36,37,38,39,189,188,190,191,186,187,15,14,16,17,12,13,236,235,237,238,239,234,278,276,279,280,281,277,209,208,204,205,206,207,5,4,1,0,2,3,83,82,78,79,80,81,432,434,433,435,436,437,566,564,565,569,567,568,531,533,532,528,530,529,523,524,522,527,525,526,503,502,501,499,500,498,329,328,327,325,326,324,587,586,585,583,584,582,555,557,556,554,553,552,379,378,380,381,382,383,414,416,415,418,419,417,626,642,624,641,625,640,615,621,620,619,692,691,688,684,667,671,675,670,677,698,284,282,285,286,287,283,139,142,140,141,138,143,221,220,216,217,218,219,274,273,275,271,270,272,197,196,192,193,194,195,147,146,148,149,144,145,153,152,154,155,150,151,158,157,159,160,161,156,179,178,174,175,176,177,230,229,231,232,233,228,452,451,450,455,453,454,603,605,604,601,600,602,426,428,427,430,431,429,445,444,446,447,448,449,443,442,441,439,440,438,456,458,457,461,459,460,593,592,591,588,590,589,595,596,594,599,597,598,385,384,386,387,388,389,494,493,492,495,496,497,647,644,648,645,646,643,651,653,650,654,697,678,682,681,672,668,676,674,683,690,109,108,110,111,112,113,117,114,118,119,116,115,100,99,101,96,97,98,65,64,60,61,62,63,127,126,128,129,130,131,247,251,246,248,249,250,19,18,20,21,22,23,56,55,57,58,59,54,43,42,44,45,46,47,68,67,69,70,71,66,346,345,347,343,344,342,479,478,477,476,474,475,370,369,371,368,366,367,339,341,340,338,336,337,516,517,518,519,520,521,359,358,357,355,356,354,462,464,463,467,465,466,318,320,319,323,321,322,365,364,363,361,362,360,406,405,407,404,402,403,609,649,611,608,606,610,652,607,636,655,663,660,662,664,658,657,659,656,661,669 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#3cc60f474fc5309f8bfdc916c4fdc0ad032cdecf3f770b83999110b499ecb4f1, 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 00:49:13 · history