Equation 677 Database

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Magma d1aae1d784d0…

magma d1aae1d784d0
Size
707
Isomorphism class hash
d1aae1d784d0005e025b8bf0847065401bac0459890504a75aee2ef7fb70555f
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 14:42:49
Display reorder
359,358,360,361,356,357,661,89,88,87,86,84,85,11,10,9,6,7,8,164,163,162,166,167,165,57,59,58,54,55,56,69,71,70,68,66,67,214,213,215,211,212,210,171,173,172,170,168,169,53,52,51,50,48,49,95,94,93,90,91,92,47,46,45,42,43,44,83,82,81,78,79,80,414,413,415,416,417,412,536,535,537,538,533,534,457,456,458,459,454,455,382,381,383,384,385,380,530,529,525,526,527,528,394,393,395,396,397,392,542,541,543,544,539,540,563,562,564,565,596,591,593,597,592,595,594,566,613,619,611,617,615,638,612,618,633,632,607,706,696,665,705,681,692,693,677,668,35,34,33,32,30,31,38,37,36,39,40,41,28,27,29,24,25,26,61,60,62,64,65,63,3,5,4,2,1,0,244,243,245,241,242,240,191,190,189,187,188,186,185,184,183,182,180,181,222,224,223,226,227,225,192,194,193,196,197,195,200,199,198,201,202,203,598,601,599,600,398,399,426,425,427,428,429,424,447,446,442,443,444,445,517,516,518,513,514,515,376,375,377,378,379,374,523,522,524,519,520,521,555,554,556,587,585,586,582,581,583,584,552,553,558,557,559,560,561,590,614,641,635,636,606,644,639,609,659,630,654,699,691,698,686,683,667,697,684,666,75,77,76,72,73,74,206,205,204,207,208,209,15,17,16,14,12,13,174,176,175,177,178,179,322,321,323,318,319,320,314,313,312,317,315,316,289,288,290,291,292,293,272,271,270,275,273,274,112,111,113,110,108,109,142,141,143,140,138,139,131,130,129,126,127,128,448,453,449,450,451,452,403,402,404,405,400,401,390,389,391,386,387,388,410,409,411,406,407,408,338,337,339,340,341,336,370,369,371,372,373,368,485,484,486,571,572,589,588,580,578,579,550,551,500,499,501,502,503,573,634,622,627,625,658,657,649,616,652,608,637,688,695,664,685,663,670,662,669,682,280,279,281,277,278,276,298,297,299,296,294,295,144,146,145,149,147,148,97,96,98,100,101,99,117,119,118,116,114,115,268,267,269,265,266,264,252,254,253,257,255,256,246,248,247,249,250,251,305,304,303,300,301,302,308,307,306,309,310,311,262,261,263,260,258,259,602,603,605,604,531,532,491,490,492,487,488,489,435,434,430,431,432,433,464,463,465,460,461,462,476,475,477,472,473,474,466,471,467,468,469,470,506,505,504,574,575,576,568,567,569,570,348,349,546,545,547,548,549,577,620,655,656,647,623,648,645,650,646,628,653,704,694,679,687,671,689,690,675,673,325,324,326,328,329,327,18,20,19,22,23,21,160,159,161,156,157,158,217,216,218,220,221,219,237,239,238,236,234,235,231,233,232,228,229,230,152,151,150,154,155,153,104,103,102,107,105,106,284,283,282,285,286,287,133,132,134,137,135,136,120,122,121,124,125,123,507,512,508,509,510,511,354,353,355,350,351,352,366,365,367,362,363,364,436,441,437,438,439,440,334,333,335,331,330,332,422,421,423,418,419,420,493,498,494,495,496,497,483,482,478,479,480,481,346,345,347,342,343,344,640,651,626,624,643,642,621,660,629,631,610,678,680,676,672,674,701,700,702,703 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#fc7d721c9159906f161771735410c214fae4809487be4161a48baf4a48d744a1, M = {90, 91, 92, 93, 94, 95, 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 2026-10-07 14:42:50 · history