Equation 677 Database

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Magma b5883d690424…

magma b5883d690424
Size
707
Isomorphism class hash
b5883d69042449365e6ed444c150b10dd17003648eb711cd26ccb38c96e1dbbc
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 05:46:27
Display reorder
102,101,103,104,113,100,706,234,236,235,238,239,237,2,0,3,4,5,1,74,73,75,70,71,72,292,291,293,289,288,290,150,155,151,152,153,154,83,82,84,85,86,87,140,139,141,142,143,138,294,297,299,298,295,296,305,304,301,300,302,303,125,124,120,121,122,123,414,413,415,416,417,418,427,426,425,430,428,429,583,582,584,585,586,587,485,487,486,484,482,483,466,465,464,467,468,469,457,456,455,453,454,452,445,444,443,442,440,441,540,539,541,536,537,538,356,358,357,354,355,353,495,494,496,497,498,499,629,606,608,607,626,628,630,627,631,625,694,695,672,685,705,699,704,702,701,696,251,247,246,249,250,248,173,172,168,169,170,171,255,254,256,257,252,253,262,261,263,258,259,260,55,54,50,51,52,53,127,126,128,129,130,131,9,8,10,11,6,7,204,209,205,206,207,208,112,63,59,60,61,62,58,57,111,56,109,110,335,337,336,340,338,339,552,551,553,555,556,554,560,562,561,559,557,558,383,385,384,388,386,387,436,435,434,431,432,433,549,548,550,545,546,547,511,510,509,508,506,507,396,395,397,398,399,400,501,500,502,505,503,504,525,524,526,527,528,529,632,636,635,633,637,634,624,623,621,622,693,703,671,668,684,678,697,680,677,673,245,240,241,243,244,242,119,118,114,115,116,117,156,161,157,158,159,160,98,97,99,94,95,96,93,92,88,89,90,91,40,39,41,36,37,38,223,222,224,225,226,227,269,268,264,265,266,267,12,17,13,14,15,16,79,78,80,81,76,77,331,330,329,333,334,332,327,326,328,324,325,323,310,309,311,312,313,314,346,345,344,342,343,341,322,321,320,317,318,319,391,390,389,393,394,392,492,491,493,489,490,488,351,350,352,347,348,349,532,531,530,533,534,535,405,404,406,401,402,403,612,618,615,616,614,617,611,609,610,613,686,700,666,665,681,687,688,689,674,679,64,66,65,68,69,67,192,197,193,194,195,196,174,179,175,176,177,178,201,200,202,203,198,199,215,214,210,211,212,213,273,272,274,275,271,270,167,166,162,163,164,165,233,232,228,229,230,231,108,49,45,46,47,48,44,43,107,105,106,42,306,307,308,566,315,316,573,575,574,543,544,542,576,578,577,581,579,580,602,600,601,604,605,603,593,592,591,589,588,590,412,411,410,408,409,407,572,571,570,569,567,568,522,521,523,518,519,520,513,512,514,517,515,516,597,599,598,596,595,594,641,640,619,639,620,638,649,651,652,650,683,698,667,669,691,676,690,692,682,675,280,277,281,278,279,276,19,18,20,21,22,23,285,284,286,287,283,282,35,34,30,31,32,33,137,136,132,133,134,135,28,27,29,24,25,26,221,220,216,217,218,219,145,144,146,147,148,149,183,182,184,185,180,181,187,186,188,189,190,191,381,380,382,377,378,379,475,474,473,472,470,471,460,459,458,462,463,461,565,564,563,439,437,438,479,481,480,477,478,476,446,448,447,451,449,450,373,372,371,376,374,375,359,361,360,364,362,363,368,370,369,366,367,365,421,420,419,423,424,422,645,648,643,654,653,655,644,647,646,642,661,670,656,657,662,660,664,663,658,659 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 = {54, 55, 56, 57, 58, 59, 145} 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 05:46:28 · history