Equation 677 Database

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Magma 389eb025e2e1…

magma 389eb025e2e1
Size
707
Isomorphism class hash
389eb025e2e12769c3247ec69a7ce46e2a34308a675630d5f71de2fdd7e9f1cc
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 01:54:38
Display reorder
237,238,239,234,235,236,706,290,289,291,292,293,288,208,207,209,204,205,206,175,174,176,177,178,179,240,245,241,242,243,244,283,282,284,285,286,287,29,28,24,25,26,27,47,46,42,43,44,45,18,23,19,20,21,22,305,304,301,300,302,303,298,299,294,296,297,295,407,406,405,410,408,409,350,349,351,348,312,313,520,519,521,516,517,518,307,308,306,311,309,310,440,439,438,443,441,442,504,506,505,509,507,508,469,468,470,471,472,473,358,357,359,360,361,362,491,490,489,487,488,486,512,511,510,515,513,514,606,607,610,609,611,608,634,635,632,633,700,674,693,703,701,690,694,704,705,702,251,250,246,247,248,249,98,97,99,100,101,96,57,56,58,59,54,55,84,89,85,86,87,88,215,214,210,211,212,213,108,113,109,110,111,112,194,193,195,196,197,192,135,134,136,137,132,133,74,73,75,76,77,72,188,187,189,190,191,186,458,457,456,461,459,460,546,547,548,549,550,551,552,553,554,555,556,557,541,542,540,545,543,544,392,391,390,389,387,388,402,404,403,401,399,400,395,394,393,397,398,396,378,380,379,377,375,376,560,558,559,562,563,561,353,347,346,345,343,344,619,620,621,617,616,615,618,628,626,627,699,691,697,685,670,671,669,676,680,684,140,139,141,142,143,138,48,53,49,50,51,52,14,13,15,16,17,12,147,146,148,149,144,145,150,155,151,152,153,154,230,229,231,232,233,228,5,4,1,0,2,3,7,6,8,9,10,11,107,106,102,103,104,105,220,219,221,216,217,218,455,454,453,452,450,451,334,336,335,333,331,332,328,330,329,327,325,326,533,532,531,528,530,529,573,575,574,571,570,572,428,427,426,430,431,429,434,433,432,436,437,435,365,364,363,367,421,366,465,467,466,464,462,463,567,569,568,565,564,566,639,623,638,624,636,637,614,630,629,622,698,695,682,688,668,678,663,686,677,692,69,68,70,71,66,67,82,81,83,78,79,80,271,270,275,272,274,273,266,264,267,268,269,265,128,127,129,130,131,126,125,124,120,121,122,123,115,114,116,117,118,119,60,65,61,62,63,64,91,90,92,93,94,95,277,281,276,278,279,280,422,423,368,354,355,356,594,595,596,597,598,599,341,340,342,337,338,339,587,586,585,582,584,583,604,603,605,600,602,601,372,374,373,371,369,370,588,589,590,591,592,593,580,579,581,577,576,578,382,381,383,384,385,386,535,536,534,537,538,539,644,651,631,641,642,643,640,653,625,654,696,675,683,681,673,672,664,689,687,679,262,261,263,259,258,260,200,199,201,202,203,198,167,166,162,163,164,165,157,156,158,159,160,161,252,253,254,255,256,257,224,223,225,226,227,222,184,183,185,180,181,182,36,41,37,38,39,40,168,173,169,170,171,172,34,33,35,30,31,32,482,481,480,485,483,484,418,417,419,420,424,425,445,444,446,447,448,449,474,476,475,479,477,478,317,319,318,314,315,316,496,495,497,492,493,494,501,503,502,500,498,499,524,523,522,526,527,525,322,321,320,323,324,352,413,412,411,416,414,415,645,649,652,648,613,647,612,650,646,655,665,659,661,667,657,658,656,662,660,666 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#5ad34b2f8758383b4965947b4701d5813e2a88f030dcc851453e9c1dba339352, M = {6, 7, 8, 9, 10, 11, 140} 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 01:54:39 · history