Equation 677 Database

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Magma 53c13cc4af72…

magma 53c13cc4af72
Size
707
Isomorphism class hash
53c13cc4af7289b9c5ed5d29b8b1d1265333082de05a4754484b8c069a19794c
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 19:51:34
Display reorder
577,576,575,573,574,572,649,213,215,214,217,218,216,127,126,128,129,130,125,3,2,4,5,1,0,24,28,33,25,26,27,140,139,141,142,143,144,72,71,73,74,75,70,287,307,235,264,298,265,305,272,291,283,277,276,296,259,32,29,30,31,60,59,61,62,63,58,98,97,99,100,101,102,496,495,494,492,493,491,543,542,544,571,546,545,567,566,565,568,569,570,336,338,337,341,339,340,332,330,331,333,334,335,400,399,401,397,398,396,388,387,389,384,385,386,437,436,435,432,433,434,381,383,382,380,378,379,624,621,607,623,622,620,640,627,608,688,689,657,669,699,706,705,703,697,704,698,306,284,292,279,273,278,297,263,219,220,221,222,83,82,84,260,304,288,303,261,184,181,182,183,169,174,170,171,172,173,92,91,93,94,95,96,233,232,234,229,230,231,206,205,201,202,203,204,21,20,22,23,18,19,15,14,16,17,12,13,35,34,36,37,38,39,351,353,352,350,348,349,359,358,357,356,354,355,343,342,344,345,346,347,364,363,365,360,361,362,552,550,549,547,551,548,541,540,539,538,536,537,372,374,373,377,375,376,476,475,474,477,478,479,457,456,458,459,460,461,609,614,634,633,613,612,631,630,632,670,696,660,655,674,686,690,687,667,685,673,65,67,66,69,64,68,57,56,52,53,54,55,124,123,119,120,121,122,107,106,136,103,104,105,131,138,132,133,134,135,252,253,254,255,256,257,266,289,299,242,267,308,280,285,281,274,309,293,295,262,197,198,199,200,193,192,194,195,196,191,76,81,77,78,79,80,590,589,588,592,593,591,487,486,578,490,488,489,559,561,560,558,556,557,447,449,448,446,444,445,443,442,441,438,439,440,599,598,597,596,594,595,431,430,429,427,428,426,600,601,604,605,603,602,390,392,391,395,393,394,629,635,641,610,636,628,639,637,638,684,701,661,659,683,694,695,677,675,682,676,45,41,40,43,44,42,271,251,310,290,249,250,302,270,245,246,247,248,244,243,269,301,268,300,294,311,286,282,258,275,208,207,209,210,211,212,228,227,223,224,225,226,86,85,87,88,89,90,188,187,189,190,185,186,239,238,240,241,236,237,175,180,176,177,178,179,452,451,450,454,455,453,480,482,481,483,484,485,408,410,409,413,411,412,467,466,465,463,464,462,470,469,468,471,472,473,529,528,527,526,524,525,405,407,406,404,402,403,530,532,531,534,535,533,366,368,367,371,369,370,606,618,615,619,617,616,625,626,611,702,691,656,679,680,693,700,678,681,692,668,7,9,8,11,6,10,116,115,117,118,113,114,315,314,316,317,313,312,318,319,320,321,322,323,149,148,150,145,146,147,155,154,156,151,152,153,50,49,51,46,47,48,160,159,161,162,157,158,137,112,108,109,110,111,328,327,329,325,324,326,166,165,167,168,163,164,425,424,423,421,422,420,515,517,516,512,513,514,497,499,498,579,580,581,518,520,519,523,521,522,554,553,555,564,562,563,587,586,585,584,582,583,508,507,506,510,511,509,503,505,504,501,502,500,415,414,416,417,418,419,642,651,643,648,647,645,644,650,646,663,672,652,653,664,665,671,662,658,666,654 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#a68686773c1c84a50fc680c2f9bbdb3f90f3c80b3d983f347231cff070658488, M = {96, 97, 98, 99, 100, 101, 135} 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 19:51:35 · history