Equation 677 Database

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Magma e62ffcecfa61…

magma e62ffcecfa61
Size
707
Isomorphism class hash
e62ffcecfa61f5929f3d3e5ba3fd97f89de8281d5bb0d4dea2df04c614b9b060
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
2026-10-09 01:49:22
Display reorder
458,463,459,460,461,462,703,246,247,249,250,251,248,228,230,229,232,233,231,201,203,202,198,199,200,216,218,217,220,221,219,327,329,328,324,325,326,2,0,1,3,4,5,213,215,214,211,212,210,223,222,224,227,225,226,241,240,242,244,245,243,205,204,206,209,207,208,238,237,239,236,234,235,529,528,530,531,532,533,485,484,486,487,482,483,481,480,476,477,478,479,471,470,472,473,474,475,377,376,378,379,374,375,522,527,523,524,525,526,465,464,466,467,468,469,563,562,564,565,596,591,593,597,592,595,594,566,660,640,643,646,645,639,641,644,647,606,642,705,685,681,702,684,668,676,706,669,67,68,70,71,69,66,78,80,79,82,83,81,283,282,284,286,287,285,164,163,162,165,166,167,101,100,99,98,96,97,63,65,64,61,62,60,121,120,122,125,123,124,319,318,320,323,321,322,72,74,73,75,76,77,135,137,136,133,134,132,130,129,131,128,126,127,601,600,598,599,456,457,358,357,359,360,361,356,518,517,519,520,521,516,551,555,550,552,553,554,506,505,507,502,503,504,500,499,501,496,497,498,549,548,559,588,581,580,584,589,579,585,556,560,343,346,344,345,342,567,621,628,659,617,627,653,626,618,616,615,633,683,682,692,698,689,693,690,700,688,7,8,10,11,9,6,107,106,105,102,103,104,18,20,19,21,22,23,314,313,312,315,316,317,16,15,17,13,14,12,38,36,37,39,40,41,269,268,267,264,265,266,93,95,94,91,92,90,310,309,311,307,308,306,110,109,108,111,112,113,25,24,26,29,27,28,365,364,366,367,362,363,436,435,437,438,433,434,536,535,537,538,539,534,354,353,355,350,351,352,429,428,430,431,432,427,495,494,490,491,492,493,515,514,558,587,577,578,583,590,582,586,557,561,449,448,445,446,447,572,607,624,620,657,609,608,650,623,612,611,658,704,686,664,661,662,670,663,665,666,195,196,192,193,194,197,298,297,299,296,294,295,158,157,156,161,159,160,273,275,274,271,272,270,114,116,115,117,118,119,257,256,255,252,253,254,146,145,144,147,148,149,171,173,172,169,170,168,190,189,191,187,188,186,292,291,293,290,288,289,138,140,139,142,143,141,602,605,603,604,546,547,512,511,513,508,509,510,405,404,406,407,408,409,395,394,396,397,392,393,410,415,411,412,413,414,402,401,403,398,399,400,349,348,347,568,569,570,576,575,573,574,488,489,425,424,426,422,423,571,625,654,634,637,629,631,630,655,638,648,651,701,667,697,699,695,696,691,694,687,151,152,154,155,153,150,35,34,33,30,31,32,54,56,55,57,58,59,47,46,45,42,43,44,178,177,179,175,176,174,184,183,185,182,180,181,302,301,300,303,304,305,260,259,258,261,262,263,50,49,48,53,51,52,85,84,86,89,87,88,278,277,276,279,280,281,450,455,451,452,453,454,389,388,390,391,386,387,332,330,333,334,335,331,341,340,336,337,338,339,382,381,383,384,385,380,371,370,372,373,368,369,442,441,443,444,439,440,543,542,544,545,541,540,417,416,418,419,420,421,635,619,649,622,652,614,656,610,632,636,613,671,672,673,677,679,678,680,675,674 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#fd7de578af0812c41995e8ffd4ad83dcb5427b7eb760f7a58401ca67989e247a, M = {90, 91, 92, 93, 94, 95, 139} 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 2026-10-09 01:49:23 · history