Equation 677 Database

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Magma 4ab6c107afae…

magma 4ab6c107afae
Size
707
Isomorphism class hash
4ab6c107afae74eba5e5d8f9f4e4d134ee0306361dd0035e0ad20883aee9ba57
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 19:08:22
Display reorder
47,46,42,43,44,45,706,83,79,78,81,82,80,265,264,266,267,268,269,125,124,120,121,122,123,16,15,17,12,13,14,73,72,74,75,76,77,186,190,191,187,188,189,19,18,20,21,22,23,62,61,63,64,65,60,193,192,194,195,196,197,249,248,250,251,246,247,603,588,605,601,597,599,592,591,590,554,552,553,315,317,316,314,312,313,308,306,307,310,311,309,456,458,457,460,461,459,511,510,512,513,514,515,373,372,374,376,377,375,516,518,517,521,519,520,432,434,433,436,437,435,447,449,448,446,444,445,626,606,622,607,629,623,610,624,618,617,694,695,673,692,704,699,701,700,705,696,95,91,90,93,94,92,271,270,272,273,274,275,204,209,205,206,207,208,277,276,278,279,280,281,233,232,228,229,230,231,173,172,168,169,170,171,6,11,7,8,9,10,263,262,258,259,260,261,221,220,216,217,218,219,110,109,111,112,113,108,530,529,528,532,533,531,367,366,368,370,371,369,337,336,338,339,340,341,468,470,469,473,471,472,343,342,344,347,345,346,326,325,324,328,329,327,332,331,330,335,333,334,581,580,579,576,578,577,488,487,486,489,490,491,503,502,501,499,500,498,640,639,637,641,635,643,644,620,619,636,697,703,674,665,685,682,688,672,690,671,1,2,0,4,5,3,29,28,24,25,26,27,200,199,201,202,203,198,103,102,104,105,106,107,55,54,56,57,58,59,67,66,68,69,70,71,114,119,115,116,117,118,87,86,88,89,84,85,185,184,180,181,182,183,256,255,257,252,253,254,602,589,604,600,596,598,595,567,593,594,568,569,349,348,350,351,352,353,427,426,428,429,430,431,441,443,442,439,440,438,465,467,466,464,462,463,356,355,354,359,357,358,452,451,450,454,455,453,584,582,583,585,586,587,322,321,323,318,319,320,627,608,625,609,628,621,612,611,613,614,689,702,667,666,680,686,683,681,677,678,283,285,284,287,282,286,210,215,211,212,213,214,131,130,126,127,128,129,225,224,226,227,222,223,234,239,235,236,237,238,133,132,134,135,136,137,165,164,166,167,162,163,176,175,177,178,179,174,96,101,97,98,99,100,245,244,240,241,242,243,550,549,551,547,546,548,543,545,544,540,541,542,505,504,506,507,508,509,566,565,564,561,563,562,365,364,363,360,361,362,481,480,482,483,484,485,492,494,493,495,496,497,555,556,557,558,559,560,474,476,475,478,479,477,573,575,574,572,571,570,632,638,631,642,630,633,634,616,615,645,691,698,668,669,687,676,684,679,693,675,144,146,145,148,149,147,33,32,34,35,30,31,160,159,161,156,157,158,289,293,288,290,291,292,294,295,296,297,298,299,138,143,139,140,141,142,155,154,150,151,152,153,39,38,40,41,36,37,302,300,303,304,305,301,50,49,51,52,53,48,525,527,526,524,522,523,417,419,418,414,415,416,395,394,393,391,392,390,379,378,380,381,382,383,421,420,422,425,423,424,400,399,401,396,397,398,536,535,534,539,537,538,410,409,408,412,413,411,407,406,405,402,403,404,388,387,389,384,385,386,646,655,647,652,651,649,648,654,650,653,661,670,656,657,662,663,660,659,664,658 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#a68686773c1c84a50fc680c2f9bbdb3f90f3c80b3d983f347231cff070658488, M = {18, 19, 20, 21, 22, 23, 142} 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 19:08:23 · history