Equation 677 Database

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Magma 28d0b6d2f6a3…

magma 28d0b6d2f6a3
Size
707
Isomorphism class hash
28d0b6d2f6a3a0ee481a8880d09a151051b2c69534e1cfc5e2ed72497c78518d
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 02:16:02
Display reorder
575,574,576,577,578,579,637,100,99,101,96,97,98,5,1,0,2,3,4,92,91,93,94,95,90,109,108,110,111,112,113,27,26,28,29,24,25,42,47,43,44,45,46,213,212,214,215,210,211,33,32,34,35,30,31,268,267,269,264,265,266,145,144,146,147,148,149,305,304,301,300,302,303,367,366,365,370,368,369,588,587,589,585,586,590,422,421,423,418,419,420,472,474,473,477,475,476,349,348,347,352,350,351,562,564,563,567,565,566,412,414,413,417,415,416,583,592,584,581,582,591,595,594,593,598,596,597,632,643,633,621,627,626,614,644,647,698,666,682,696,677,700,697,691,702,705,706,237,236,238,239,234,235,82,83,78,79,80,81,142,141,143,138,139,140,205,204,206,207,208,209,254,253,255,256,257,252,41,40,36,37,38,39,279,278,280,281,276,277,261,260,262,263,258,259,124,123,125,120,121,122,128,127,129,130,131,126,10,9,11,6,7,8,428,427,429,425,426,424,443,442,444,445,446,447,450,449,448,452,453,451,441,440,439,437,438,436,344,346,345,341,342,343,434,433,435,430,431,432,456,455,454,458,459,457,528,527,526,530,531,529,478,480,479,481,482,483,617,615,616,618,649,648,608,642,609,683,684,694,678,661,668,665,669,679,690,699,290,289,291,292,293,288,73,74,75,76,77,72,13,12,14,15,16,17,285,284,286,287,282,283,166,165,167,162,163,164,199,198,200,201,202,203,69,68,70,71,66,67,18,23,19,20,21,22,102,107,103,104,105,106,243,242,244,245,240,241,56,55,57,58,59,54,580,390,389,391,392,393,465,464,463,461,462,460,361,360,359,363,364,362,568,570,569,573,571,572,353,355,354,356,357,358,605,604,603,601,602,600,497,496,498,499,500,501,561,560,559,557,558,556,554,553,555,551,552,550,612,646,630,645,628,622,629,624,625,695,680,689,692,657,667,676,663,687,675,701,273,272,274,275,270,271,191,186,187,188,189,190,60,65,61,62,63,64,311,310,306,307,308,309,230,229,231,232,233,228,313,312,314,315,316,317,298,297,299,294,295,296,169,168,170,171,172,173,250,249,251,246,247,248,51,50,52,53,48,49,88,87,89,84,85,86,396,395,394,399,397,398,470,469,471,466,467,468,484,486,485,489,487,488,544,546,545,549,547,548,510,509,508,513,511,512,400,402,401,405,403,404,523,525,524,522,520,521,515,514,516,517,518,519,492,491,490,495,493,494,611,619,620,613,607,610,623,651,650,703,673,685,704,662,674,681,658,688,686,693,158,157,159,160,161,156,220,221,216,217,218,219,185,184,180,181,182,183,193,192,194,195,196,197,326,328,327,324,325,329,133,132,134,135,136,137,154,153,155,150,151,152,321,320,322,323,319,318,226,225,227,222,223,224,117,116,118,119,114,115,177,176,178,179,174,175,506,505,507,503,504,502,333,332,330,334,331,599,537,536,535,539,540,538,340,339,338,336,337,335,542,541,543,533,534,532,409,411,410,408,406,407,380,382,381,379,377,378,373,372,371,375,376,374,388,387,386,385,383,384,641,640,636,606,638,634,635,631,639,672,656,660,670,653,654,655,652,664,659,671 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#5ad34b2f8758383b4965947b4701d5813e2a88f030dcc851453e9c1dba339352, M = {114, 115, 116, 117, 118, 119, 135} 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 02:16:03 · history