Equation 677 Database

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Magma 0128607c955e…

magma 0128607c955e
Size
707
Isomorphism class hash
0128607c955eead81194fecb99796585326c32af193731657e2a33deaf2287e9
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
2026-10-07 04:25:54
Display reorder
112,111,113,108,109,110,706,181,183,180,182,185,184,73,72,74,75,76,77,187,191,186,188,189,190,30,35,31,32,33,34,71,70,66,67,68,69,7,6,8,9,10,11,43,42,44,45,46,47,247,269,291,251,282,268,250,290,281,258,259,246,255,275,192,193,194,237,379,378,380,383,381,382,375,377,376,372,373,374,329,328,327,324,325,326,514,513,515,512,510,511,449,448,447,445,446,444,403,402,404,406,407,405,556,555,557,552,554,553,452,451,450,455,453,454,371,370,369,367,368,366,385,384,386,388,389,387,607,610,611,609,612,608,620,617,615,616,696,665,675,700,704,702,703,701,705,697,136,133,137,132,135,134,78,83,79,80,81,82,235,230,276,254,236,285,257,277,256,195,196,238,213,212,214,240,278,260,288,244,232,243,287,233,92,91,93,94,95,90,138,143,139,140,141,142,101,100,96,97,98,99,174,175,176,177,178,179,319,318,320,323,321,322,438,440,439,441,442,443,332,331,330,333,334,335,352,351,353,350,348,349,310,309,311,307,306,308,359,358,357,356,354,355,396,398,397,399,400,401,563,562,561,560,559,558,550,549,551,546,547,548,420,422,421,423,424,425,625,623,626,606,624,622,614,619,637,639,698,682,678,677,691,693,692,669,694,668,221,218,217,216,220,219,52,51,53,48,49,50,13,12,14,15,16,17,227,226,223,222,224,225,54,59,55,56,57,58,19,18,20,21,22,23,63,62,64,65,60,61,261,263,215,241,279,262,242,267,280,264,265,266,231,286,197,198,199,239,470,469,468,471,472,473,591,593,592,589,588,590,580,579,581,578,577,576,457,456,458,461,459,460,597,599,598,596,595,594,602,600,601,605,603,604,462,464,463,465,466,467,390,392,391,393,394,395,586,585,587,583,582,584,571,572,570,573,574,575,641,632,635,643,642,636,645,633,634,644,695,676,671,674,673,699,685,684,681,683,248,284,292,252,274,273,173,172,169,168,170,171,245,228,283,270,271,272,253,293,289,234,229,249,84,89,85,86,87,88,24,29,25,26,27,28,210,209,211,207,206,208,37,36,38,39,40,41,128,127,129,130,131,126,205,204,201,200,202,203,409,408,410,413,411,412,436,435,437,433,434,432,415,414,416,419,417,418,315,317,316,313,314,312,431,430,429,427,428,426,568,567,569,564,566,565,507,509,508,504,505,506,341,340,339,338,336,337,347,346,345,343,344,342,360,362,361,363,364,365,627,630,628,621,631,629,613,640,638,618,689,666,670,679,687,688,686,680,690,672,144,147,145,146,149,148,160,159,161,156,157,158,2,1,3,4,5,0,299,298,295,294,296,297,119,118,114,115,116,117,120,125,121,122,123,124,104,103,105,106,107,102,155,154,150,151,152,153,305,304,301,300,302,303,165,164,166,167,162,163,523,522,524,527,525,526,475,474,476,478,479,477,500,499,498,501,502,503,541,540,542,545,543,544,536,535,534,538,539,537,521,520,519,518,516,517,530,529,528,533,531,532,480,482,481,483,484,485,488,487,486,490,491,489,492,494,493,495,496,497,646,655,647,652,651,649,648,654,650,653,661,656,657,662,663,667,660,659,664,658 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 = {30, 31, 32, 33, 34, 35, 137} 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 2026-10-07 04:25:55 · history