Equation 677 Database

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Magma 0f7c92cd4e0e…

magma 0f7c92cd4e0e
Size
707
Isomorphism class hash
0f7c92cd4e0eddbcb2eefe47227f64b35bb295d4375c82c742ee2abb0e8608d2
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 13:15:14
Display reorder
561,560,557,556,558,559,696,149,148,145,146,144,147,213,215,214,211,212,210,281,280,279,277,278,276,266,265,264,269,267,268,8,7,6,11,9,10,107,106,105,104,102,103,62,60,61,63,64,65,270,272,271,273,274,275,55,56,54,59,57,58,151,150,152,155,153,154,108,110,109,111,112,113,467,466,468,469,464,465,398,397,393,394,395,396,388,387,389,390,391,392,490,489,491,492,493,488,413,412,414,415,416,411,370,369,371,372,373,374,483,482,484,485,486,487,563,562,564,565,596,591,593,597,592,595,594,566,648,628,621,607,627,649,620,650,638,616,615,705,704,677,678,706,663,671,674,662,199,198,201,202,203,200,243,245,244,241,242,240,320,319,318,322,323,321,299,298,297,296,294,295,115,114,116,118,119,117,250,249,251,247,248,246,236,235,234,237,238,239,140,139,138,143,141,142,289,288,290,291,292,293,315,317,316,313,314,312,287,286,285,284,282,283,605,604,602,603,538,539,441,440,442,437,438,439,435,434,436,431,432,433,410,409,405,406,407,408,399,404,400,401,402,403,421,420,422,423,424,419,552,551,553,585,586,584,587,590,588,589,554,555,331,330,332,333,334,567,653,658,651,622,636,626,644,659,643,652,642,701,697,665,667,661,666,691,668,664,311,310,307,308,306,309,121,120,122,125,123,124,28,27,29,24,25,26,134,133,132,137,135,136,127,126,128,130,131,129,46,45,47,42,44,43,175,174,176,179,177,178,93,95,94,90,91,92,159,161,160,158,156,157,230,229,228,231,232,233,5,4,3,2,1,0,346,345,341,342,343,344,541,545,540,542,543,544,427,426,428,429,430,425,515,514,516,517,512,513,528,527,529,530,531,526,500,505,501,502,503,504,549,548,550,581,582,583,571,570,572,573,418,417,354,353,355,356,357,568,625,641,606,624,657,618,614,610,623,629,632,703,699,673,698,700,672,690,689,681,204,206,209,207,208,205,49,50,48,52,53,51,221,220,219,217,218,216,99,101,100,96,97,98,164,163,162,167,165,166,193,192,194,196,197,195,21,23,22,18,20,19,252,254,253,255,256,257,302,301,300,304,305,303,329,328,327,324,325,326,258,260,259,261,262,263,601,600,598,599,518,519,377,376,378,379,380,375,522,521,523,524,525,520,473,472,474,475,470,471,496,495,497,498,499,494,457,456,452,453,454,455,450,449,451,574,575,576,580,579,577,578,546,547,361,360,362,358,359,569,619,660,647,630,637,645,634,639,613,655,609,702,695,692,670,694,680,669,679,693,78,80,83,81,82,79,68,67,66,69,70,71,183,185,184,182,180,181,37,36,38,40,41,39,75,77,76,72,73,74,186,188,187,189,190,191,226,225,227,224,222,223,173,172,171,170,168,169,32,31,30,34,35,33,14,12,13,15,16,17,88,87,89,85,86,84,532,533,534,535,536,537,363,368,364,365,366,367,339,338,340,335,336,337,348,347,349,350,351,352,445,444,446,447,448,443,459,458,460,461,462,463,508,507,509,510,511,506,479,478,480,481,476,477,385,384,386,381,382,383,612,608,617,654,656,631,633,646,635,611,640,683,682,688,676,687,685,675,686,684 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#53d992532d406ee1a16d046074f6b11dc06c8f5c6df8c27dc9277719dd794878, M = {102, 103, 104, 105, 106, 107, 145} 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 13:15:17 · history