Equation 677 Database

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Magma aff10199e996…

magma aff10199e996
Size
707
Isomorphism class hash
aff10199e996b851e623300868f530311dc15de08e431cfa8173f702e5c1a13f
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
2026-10-07 01:33:11
Display reorder
223,222,224,225,226,227,706,286,285,283,282,284,287,130,129,131,126,127,128,276,277,278,279,280,281,179,178,174,175,176,177,92,91,93,94,95,90,192,197,193,194,195,196,308,307,309,310,311,306,312,317,313,314,315,316,330,335,331,332,333,334,250,249,251,247,246,248,216,221,217,218,219,220,376,375,377,373,374,372,445,444,446,449,447,448,392,391,390,393,394,395,600,601,602,605,603,604,528,530,529,532,533,531,403,402,404,406,407,405,381,383,382,380,378,379,463,462,464,467,465,466,506,505,504,508,509,507,629,628,626,618,625,627,630,633,612,685,662,686,698,699,704,705,702,695,700,703,294,299,296,297,298,295,293,292,288,289,290,291,303,302,304,305,300,301,209,208,204,205,206,207,16,15,17,12,13,14,7,6,8,9,10,11,18,23,19,20,21,22,125,124,120,121,122,123,119,118,114,115,116,117,108,113,109,110,111,112,132,137,133,134,135,136,369,371,370,366,367,368,555,557,556,553,554,552,346,345,347,344,342,343,348,350,349,352,353,351,560,559,558,561,562,563,566,565,564,569,567,568,422,421,420,424,425,423,435,437,436,433,434,432,582,583,584,585,586,587,609,610,606,622,624,623,620,631,621,663,678,693,673,671,677,688,690,659,672,691,155,154,151,152,153,150,149,148,144,145,146,147,0,1,2,3,4,5,159,158,160,161,156,157,139,138,140,141,142,143,163,162,164,165,166,167,261,260,262,263,258,259,268,267,269,264,265,266,275,274,270,271,272,273,215,214,210,211,212,213,84,89,85,86,87,88,546,548,547,549,550,551,596,594,595,597,598,599,461,460,459,456,457,458,511,510,512,515,513,514,363,365,364,361,362,360,516,518,517,519,520,521,522,524,523,527,525,526,589,590,588,592,593,591,442,441,443,438,439,440,616,607,613,619,614,617,608,632,615,669,670,694,689,674,683,697,675,676,660,687,80,79,82,83,78,81,229,228,230,231,232,233,239,238,234,235,236,237,243,242,244,245,240,241,255,254,256,257,252,253,51,50,52,53,48,49,55,54,56,57,58,59,43,42,44,45,46,47,67,66,68,69,70,71,62,61,63,64,65,60,74,73,75,76,77,72,581,580,579,578,576,577,339,341,340,336,338,337,468,470,469,472,473,471,428,427,426,429,430,431,498,500,499,502,503,501,488,487,486,491,489,490,494,493,492,496,497,495,485,484,483,480,481,482,478,477,479,474,475,476,645,644,642,643,641,636,611,634,635,696,661,684,701,679,680,692,668,681,667,682,189,188,191,186,187,190,28,27,29,24,25,26,319,323,318,320,321,322,35,34,30,31,32,33,104,103,105,106,107,102,37,36,38,39,40,41,173,172,168,169,170,171,324,325,326,327,328,329,181,180,182,183,184,185,98,97,99,100,101,96,199,198,200,201,202,203,542,541,540,545,543,544,537,539,538,535,536,534,452,451,450,453,454,455,357,359,358,355,356,354,412,411,413,410,408,409,384,386,385,387,388,389,397,396,398,399,400,401,414,416,415,418,419,417,571,570,572,573,574,575,649,646,647,648,650,638,637,639,640,655,651,666,664,656,652,665,658,654,653,657 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#83fb73755ed07f789756511d0e776415c2bd28bb0aaa387c6c265081499d5ced, M = {54, 55, 56, 57, 58, 59, 141} 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 2026-10-07 01:33:16 · history