Equation 677 Database

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Magma 4c9c3ae6c1f9…

magma 4c9c3ae6c1f9
Size
707
Isomorphism class hash
4c9c3ae6c1f9d8c8bf0124d2a1e7e8b5a493292af20f90215f90c0204e5657d7
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
2026-10-08 14:03:13
Display reorder
492,494,493,491,489,490,634,123,122,124,125,120,121,183,184,185,180,181,182,45,44,46,47,42,43,86,85,87,88,89,84,231,230,232,233,228,229,245,244,241,240,242,243,144,149,145,146,147,148,238,237,239,235,234,236,142,141,143,138,139,140,117,116,118,119,114,115,315,314,316,317,313,312,528,530,529,525,526,527,507,509,508,512,510,511,396,398,397,401,399,400,386,385,384,389,387,388,445,444,446,447,448,449,439,438,440,441,442,443,393,395,394,392,390,391,513,515,514,518,516,517,378,380,379,381,382,383,608,609,611,612,607,610,638,645,647,699,670,677,697,676,696,698,688,704,705,706,112,111,113,108,109,110,255,256,257,252,253,254,246,251,247,248,249,250,137,136,132,133,134,135,294,295,296,297,298,299,151,150,152,153,154,155,1,5,0,2,3,4,209,208,204,205,206,207,157,156,158,159,160,161,95,94,90,91,92,93,99,98,100,101,96,97,402,404,403,405,406,407,570,571,572,573,574,575,413,412,411,409,410,408,414,416,415,417,418,419,502,501,503,504,505,506,334,333,335,331,330,332,470,469,468,472,473,471,590,588,589,592,593,591,577,578,576,579,580,581,637,639,635,632,648,649,642,636,640,683,680,687,681,659,666,668,671,682,691,700,102,107,103,104,105,106,23,18,19,20,21,22,269,268,265,264,266,267,227,226,222,223,224,225,174,179,175,176,177,178,127,126,128,129,130,131,48,53,49,50,51,52,195,194,196,197,192,193,186,191,187,188,189,190,60,65,61,62,63,64,199,198,200,201,202,203,425,424,423,422,420,421,478,477,479,474,475,476,561,563,562,560,559,558,480,482,481,483,484,485,601,602,600,605,603,604,463,462,464,465,466,467,534,535,536,537,538,539,520,519,521,522,523,524,582,583,584,586,587,585,613,646,614,644,616,615,631,641,643,692,675,690,694,658,667,678,660,693,684,701,280,279,281,276,277,278,275,270,271,272,273,274,56,55,57,58,59,54,309,308,310,311,306,307,214,213,215,210,211,212,300,301,302,303,304,305,165,164,166,167,162,163,13,12,14,15,16,17,69,68,70,71,66,67,171,170,172,173,168,169,261,260,262,263,259,258,362,361,360,365,363,364,542,544,543,541,540,545,568,567,569,565,564,566,553,554,552,555,556,557,437,436,435,433,434,432,499,498,500,495,496,497,547,548,546,551,549,550,533,532,531,487,488,486,595,596,594,597,598,599,627,606,626,629,633,628,630,651,650,702,669,679,703,661,665,685,664,689,686,695,30,35,31,32,33,34,76,77,72,73,74,75,79,78,80,81,82,83,11,10,6,7,8,9,326,328,327,324,325,329,290,288,291,292,293,289,27,26,28,29,24,25,323,322,319,318,320,321,216,221,217,218,219,220,41,40,36,37,38,39,287,286,283,282,284,285,428,427,426,431,429,430,355,354,356,357,358,359,368,367,366,370,371,369,374,373,372,377,375,376,452,451,450,454,455,453,458,457,456,460,461,459,347,346,345,343,344,342,351,353,352,350,348,349,336,338,337,339,340,341,618,620,619,622,623,621,617,624,625,674,656,663,672,652,653,655,654,662,657,673 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 = {78, 79, 80, 81, 82, 83, 133} 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 2026-10-08 14:03:19 · history