Equation 677 Database

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Magma 78f0b3a34bfd…

magma 78f0b3a34bfd
Size
707
Isomorphism class hash
78f0b3a34bfdcb967b0b4ab352df3bca31e96e27f942aa3644470478771b6bb2
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 08:51:49
Display reorder
419,424,420,421,422,423,688,236,235,237,238,239,234,127,126,128,130,131,129,225,227,226,223,224,222,137,136,135,132,133,134,183,185,184,182,180,181,186,188,187,189,190,191,228,230,229,232,233,231,260,259,258,261,262,263,245,244,243,240,241,242,249,251,250,246,247,248,140,139,138,143,141,142,428,427,429,430,425,426,495,494,496,492,491,493,507,506,508,504,503,505,380,379,381,382,377,378,431,436,432,433,434,435,401,406,402,403,404,405,353,358,354,355,356,357,563,562,564,565,596,591,593,597,592,595,594,566,625,660,657,626,645,634,644,624,643,642,633,690,706,661,668,662,705,663,695,669,114,115,119,117,118,116,57,59,58,54,55,56,47,46,45,42,43,44,28,27,29,26,24,25,120,121,122,123,124,125,51,53,52,48,49,50,62,61,60,63,64,65,282,284,283,286,287,285,315,317,316,313,314,312,320,319,318,323,321,322,272,271,270,275,273,274,600,599,601,598,523,524,414,413,415,416,417,418,478,477,473,474,475,476,470,469,471,472,467,468,388,387,383,384,385,386,407,412,408,409,410,411,545,544,546,573,574,575,586,585,583,584,552,553,339,338,340,337,336,567,608,650,655,648,656,612,623,613,614,611,622,704,698,679,675,683,693,684,682,687,252,254,256,257,255,253,218,217,216,221,219,220,30,32,31,34,35,33,68,67,66,69,70,71,81,83,82,80,78,79,278,277,276,281,279,280,155,154,153,150,151,152,288,290,289,292,293,291,106,105,107,104,102,103,167,166,165,164,162,163,306,308,307,309,310,311,530,529,526,525,527,528,330,331,332,333,334,335,517,515,518,519,520,516,499,497,500,501,502,498,360,359,361,362,363,364,369,368,370,365,366,367,550,549,551,582,580,581,572,571,569,570,542,543,558,557,559,560,561,590,615,651,620,654,630,649,646,641,628,636,616,691,699,696,674,664,697,692,678,686,298,297,296,294,295,299,91,90,92,94,95,93,173,172,171,168,169,170,212,210,211,213,214,215,195,197,196,194,193,192,40,39,41,37,38,36,1,2,0,4,5,3,9,11,10,7,8,6,267,269,268,265,266,264,84,86,85,87,88,89,74,73,72,77,75,76,603,602,604,605,522,521,533,531,534,535,536,532,451,450,452,453,454,449,456,455,457,458,459,460,392,391,393,394,389,390,480,479,481,482,483,484,556,555,554,589,588,587,577,576,578,579,547,548,538,537,539,540,541,568,639,606,647,640,617,610,652,618,658,631,635,689,681,680,666,667,685,694,676,665,206,205,207,208,209,204,329,328,327,326,324,325,21,23,22,19,20,18,203,202,201,198,199,200,113,112,111,109,110,108,12,14,13,15,16,17,96,98,97,100,101,99,149,148,147,144,145,146,176,175,174,177,178,179,160,159,161,157,158,156,304,303,305,301,302,300,465,464,466,461,462,463,346,345,341,342,343,344,487,486,488,489,490,485,348,347,349,350,351,352,399,398,400,395,396,397,510,514,509,511,512,513,439,438,440,441,442,437,443,448,444,445,446,447,376,375,371,372,373,374,637,627,632,653,629,609,638,659,619,607,621,671,672,703,700,702,701,673,677,670 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 = {84, 85, 86, 87, 88, 89, 144} 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 08:51:51 · history