Equation 677 Database

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Magma 8db1de844456…

magma 8db1de844456
Size
707
Isomorphism class hash
8db1de844456d925ae1bdaaa1ee4f0bd047c00ca2ad7bc5c4c0e60e8b1048706
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 12:31:44
Display reorder
256,255,254,252,253,257,656,175,174,176,178,179,177,279,281,280,277,278,276,230,229,228,231,232,233,247,246,248,249,250,251,117,119,118,114,115,116,163,162,164,167,165,166,1,2,0,4,5,3,244,243,245,242,240,241,171,173,172,168,169,170,302,300,301,305,303,304,388,387,389,384,385,386,477,476,478,479,474,475,481,480,482,483,484,485,543,542,544,545,540,541,457,456,458,459,460,461,537,536,538,539,534,535,602,601,603,604,605,600,564,569,565,566,567,568,394,393,395,390,391,392,587,586,583,582,584,585,610,616,611,607,609,619,634,623,638,648,692,704,674,676,670,675,693,687,658,706,24,26,25,27,28,29,142,141,143,140,138,139,6,8,7,10,11,9,22,21,23,18,19,20,267,269,268,264,265,266,77,76,75,72,73,74,13,12,14,17,15,16,56,55,54,57,58,59,189,191,190,186,187,188,185,184,183,182,180,181,414,419,415,416,417,418,469,468,470,471,472,473,429,428,430,431,426,427,555,554,556,557,552,553,432,437,433,434,435,436,374,373,375,376,377,372,503,502,498,499,500,501,378,383,379,380,381,382,370,369,371,366,367,368,363,362,364,365,360,361,639,650,640,635,647,655,628,622,632,642,669,657,673,667,686,659,660,690,663,679,193,192,194,196,197,195,263,262,261,258,259,260,69,71,70,67,68,66,145,144,146,147,148,149,153,155,154,150,151,152,65,64,63,60,61,62,210,212,211,214,215,213,104,103,102,105,106,107,137,136,135,134,132,133,109,108,110,112,113,111,446,445,447,448,449,444,560,559,561,562,563,558,316,315,317,312,313,314,320,319,321,322,323,318,398,397,399,400,401,396,574,573,575,570,571,572,507,506,508,509,504,505,344,343,345,346,347,342,352,351,353,348,349,350,338,337,339,340,341,336,641,653,644,630,645,652,624,617,637,633,694,662,691,688,664,684,682,671,677,681,283,282,284,286,287,285,124,123,125,122,120,121,88,87,89,86,84,85,236,235,234,238,239,237,216,218,217,219,220,221,81,83,82,79,80,78,41,40,39,36,37,38,271,270,272,275,273,274,35,34,33,32,30,31,46,47,45,44,43,42,516,521,517,518,519,520,329,328,324,325,326,327,529,528,530,531,532,533,551,550,546,547,548,549,488,487,489,490,491,486,412,411,413,408,409,410,453,452,454,455,450,451,467,466,462,463,464,465,423,422,424,425,420,421,407,406,402,403,404,405,643,651,649,629,646,654,626,621,631,636,666,661,668,685,678,665,672,689,683,680,96,98,97,99,100,101,199,198,200,203,201,202,157,156,158,161,159,160,92,91,90,94,95,93,52,51,53,49,50,48,204,206,205,208,209,207,129,131,130,127,128,126,293,292,291,289,288,290,222,224,223,225,226,227,295,296,294,297,298,299,330,335,331,332,333,334,440,439,441,442,443,438,576,577,578,579,580,581,307,311,306,308,309,310,359,358,354,355,356,357,492,497,493,494,495,496,594,599,595,596,597,598,513,512,514,515,510,511,526,525,527,522,523,524,592,591,593,588,589,590,608,620,612,606,614,627,613,615,625,618,701,703,700,699,702,695,697,696,698,705 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#141a5ad98d093a51cbcd8d0e5f762ac857a7d54b6447f4e2b6939d4d1af2e3e9, M = {0, 1, 2, 3, 4, 5, 132} 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 12:31:45 · history