Equation 677 Database

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Magma 9fe9a4eefdda…

magma 9fe9a4eefdda
Size
707
Isomorphism class hash
9fe9a4eefdda7f908b296acd858a858ac469d7fb3d0fb7d5c4a99645176ed702
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
2026-10-06 19:13:41
Display reorder
403,402,404,405,406,407,639,302,304,303,300,301,305,293,292,288,289,290,291,179,178,174,175,176,177,162,167,163,164,165,166,317,316,312,313,314,315,191,190,186,187,188,189,111,110,112,113,108,109,61,60,62,63,64,65,53,52,48,49,50,51,85,84,86,87,88,89,99,98,100,101,96,97,115,114,116,117,118,119,549,548,550,546,547,545,361,362,360,363,364,365,366,368,367,369,370,371,534,533,535,538,536,537,556,555,554,553,551,552,400,399,401,398,396,397,563,565,564,568,566,567,390,392,391,394,395,393,627,630,631,633,634,628,632,635,691,695,653,692,690,652,704,698,702,706,697,703,271,273,272,275,270,274,29,28,24,25,26,27,201,200,202,203,198,199,287,286,282,283,284,285,13,12,14,15,16,17,260,259,261,262,263,258,247,246,248,249,250,251,5,4,1,0,2,3,237,236,238,239,234,235,335,334,330,331,332,333,35,34,30,31,32,33,129,128,130,131,126,127,530,532,531,527,528,529,486,485,487,489,524,488,463,462,464,466,467,465,458,457,456,459,460,461,476,475,474,478,477,525,603,605,604,600,602,601,511,510,512,507,508,509,521,520,519,522,523,526,623,621,622,624,626,625,636,629,687,689,674,677,685,650,686,673,688,701,676,675,94,90,95,92,93,91,103,102,104,105,106,107,80,79,81,82,83,78,46,45,47,42,43,44,56,55,57,58,59,54,68,67,69,70,71,66,344,342,345,346,347,343,294,299,295,296,297,298,168,173,169,170,171,172,160,159,161,156,157,158,77,76,72,73,74,75,181,180,182,183,184,185,577,578,576,579,580,581,574,573,572,571,569,570,388,387,389,385,386,384,584,582,583,585,586,587,590,588,589,593,591,592,561,560,562,559,557,558,541,540,539,543,544,542,598,597,599,596,595,594,615,612,616,611,613,617,620,637,667,699,672,681,671,648,679,683,680,694,657,666,124,120,125,122,123,121,232,231,233,228,229,230,337,336,341,338,340,339,241,240,242,243,244,245,252,257,253,254,255,256,37,36,38,39,40,41,306,311,307,308,309,310,326,325,327,328,329,324,264,269,265,266,267,268,322,321,323,318,319,320,277,276,278,279,280,281,196,195,197,192,193,194,505,506,575,502,503,504,444,446,445,447,448,449,451,450,452,454,455,453,515,514,513,516,517,518,496,498,497,499,500,501,491,490,492,495,493,494,479,481,480,484,482,483,472,471,473,470,468,469,607,610,608,609,619,606,618,614,664,705,656,696,665,649,684,682,669,700,668,670,356,358,357,355,354,359,6,11,7,8,9,10,19,18,20,21,22,23,219,218,220,221,216,217,349,350,348,351,352,353,150,155,151,152,153,154,138,143,139,140,141,142,146,145,147,148,149,144,206,205,207,208,209,204,132,137,133,134,135,136,227,226,222,223,224,225,212,211,213,214,215,210,429,431,430,426,427,428,434,433,432,437,435,436,409,408,410,412,413,411,383,382,381,378,379,380,377,376,375,374,372,373,417,419,418,415,416,414,438,440,439,443,441,442,422,421,420,423,424,425,646,640,643,641,644,645,642,638,661,693,655,662,678,647,658,660,659,663,654,651 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#7c5787f3763007370795fcf378d2af7959e084037efbb89592fd99450acc2142, M = {102, 103, 104, 105, 106, 107, 127} 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 2026-10-06 19:13:42 · history