Equation 677 Database

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Magma ec949ac7a6c2…

magma ec949ac7a6c2
Size
707
Isomorphism class hash
ec949ac7a6c2b48c1241dc5040ade1cc1f71f28690cb123e72a85d9c0bc83b28
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 14:29:43
Display reorder
501,500,502,499,497,498,648,94,97,95,96,99,98,196,195,197,198,199,194,239,238,234,235,236,237,166,171,167,168,169,170,31,30,32,27,28,29,202,201,203,204,205,200,288,304,247,268,302,259,306,273,292,284,276,277,297,262,212,213,214,215,182,181,183,178,179,180,46,45,47,48,49,50,419,418,417,414,415,416,594,596,595,597,598,599,370,369,371,368,366,367,589,588,587,591,592,590,353,352,351,350,348,349,553,552,551,556,554,555,550,549,548,547,545,546,533,535,534,538,536,537,521,523,522,524,525,526,636,637,614,626,638,615,627,639,628,685,690,654,670,696,706,704,703,697,705,698,308,280,293,285,274,281,303,269,248,249,250,251,253,252,254,270,309,289,300,265,230,231,232,233,101,100,102,103,104,105,111,110,106,107,108,109,11,16,12,13,14,15,226,225,227,222,223,224,66,65,61,62,63,64,5,10,6,7,8,9,186,185,187,188,189,184,372,374,373,376,377,375,512,514,513,509,510,511,422,421,420,423,424,425,574,576,575,573,571,572,586,433,432,434,435,436,363,365,364,360,361,362,341,340,339,338,336,337,444,443,445,446,447,448,455,457,456,458,459,460,607,608,629,606,630,610,632,612,620,667,699,660,657,675,687,691,692,669,686,678,58,60,80,59,57,56,51,78,52,53,54,55,3,2,4,1,0,79,42,41,43,44,39,40,36,35,37,38,33,34,86,85,87,82,83,84,266,287,301,246,267,307,278,283,279,272,305,291,295,261,190,191,192,193,174,173,175,176,177,172,89,88,90,91,92,93,403,402,404,407,405,406,527,529,528,530,531,532,542,544,543,540,541,539,400,399,401,396,397,398,393,395,394,390,391,392,515,517,516,518,519,520,381,383,382,378,379,380,602,600,601,604,605,603,409,408,410,412,413,411,623,624,641,621,625,622,611,613,640,681,701,661,659,682,693,695,673,676,680,674,72,69,67,68,71,70,271,257,310,290,255,256,296,260,19,20,17,18,229,228,264,299,263,298,294,311,286,282,258,275,121,120,122,123,118,119,24,23,25,26,21,22,242,241,243,244,245,240,81,77,73,74,75,76,113,112,114,115,116,117,217,216,218,219,220,221,593,566,567,570,568,569,451,450,449,454,452,453,385,384,386,389,387,388,557,558,565,561,559,560,462,461,463,465,466,464,442,441,440,439,437,438,429,431,430,426,427,428,330,331,332,333,334,335,358,357,359,355,356,354,617,616,619,631,609,618,634,635,633,702,689,656,679,683,694,700,677,684,688,668,126,129,127,128,125,124,130,135,131,132,133,134,317,316,313,312,314,315,322,321,323,319,318,320,158,157,159,154,155,156,153,152,148,149,150,151,144,143,145,146,147,142,165,164,160,161,162,163,206,211,207,208,209,210,328,327,329,325,324,326,139,138,140,141,136,137,486,485,487,490,488,489,346,345,347,343,344,342,584,583,585,562,563,564,504,503,505,506,507,508,475,474,473,478,476,477,481,480,479,484,482,483,582,581,580,579,577,578,471,470,472,467,468,469,492,491,493,495,496,494,642,651,643,647,645,644,650,646,649,663,672,652,653,664,665,671,662,658,666,655 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#d668bf04c36f8b4c67728650c5c82a046d470936a3c130394e60cdea0aa42f4e, M = {84, 85, 86, 87, 88, 89, 129} 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 14:29:44 · history