Equation 677 Database

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Magma 0c2a393565fc…

magma 0c2a393565fc
Size
707
Isomorphism class hash
0c2a393565fc9dd68affd500fab8ad216f6727c2ad10ca7c9d2ab8816de837c3
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 22:09:43
Display reorder
604,605,601,600,602,603,706,560,593,569,586,542,574,325,343,348,320,338,529,581,527,599,334,538,556,316,561,594,588,564,587,543,575,326,344,349,321,339,528,576,525,317,335,539,557,562,595,589,565,582,544,570,327,345,350,322,340,530,577,523,312,330,535,553,563,596,590,566,583,545,571,328,346,351,323,341,531,578,524,313,331,534,552,559,597,591,567,584,541,572,329,347,352,318,336,532,579,522,314,332,536,554,558,598,592,568,585,540,573,324,342,353,319,337,533,580,526,315,333,537,555,549,551,547,546,548,550,626,630,629,631,628,627,699,700,703,705,702,701,704,654,653,655,656,659,658,657,132,153,290,470,210,477,359,101,156,297,129,68,122,415,375,139,52,430,45,133,376,154,291,471,211,478,354,96,157,298,130,69,123,414,46,140,53,431,134,377,155,292,472,212,479,355,97,158,299,131,70,124,416,47,141,48,427,135,372,150,293,473,213,474,356,98,159,294,126,71,125,417,42,142,49,426,136,373,151,288,469,214,475,357,99,160,295,127,66,120,418,43,143,50,428,137,374,152,289,468,215,476,358,100,161,296,128,67,121,419,44,138,51,429,360,362,363,364,365,361,673,668,660,670,661,672,651,647,646,650,652,649,648,682,681,678,679,680,683,684,73,280,244,18,460,269,464,28,282,246,410,35,370,174,38,10,406,54,17,74,39,281,245,19,461,264,465,29,283,247,411,30,371,175,12,11,407,55,75,40,276,240,20,457,265,466,24,284,248,412,31,366,176,13,6,403,56,76,41,277,241,21,456,266,467,25,285,249,413,32,367,177,14,7,402,57,77,36,278,242,22,458,267,462,26,286,250,409,33,368,178,15,8,404,58,72,37,279,243,23,459,268,463,27,287,251,408,34,369,179,16,9,405,59,273,275,270,271,272,274,664,662,663,665,677,676,633,642,636,637,641,643,635,689,693,685,695,698,697,691,196,169,380,302,259,257,221,309,167,387,453,113,205,233,104,198,86,145,91,197,105,170,381,303,260,252,216,310,162,388,454,108,206,228,92,199,87,146,192,106,171,382,304,261,253,217,311,163,389,455,109,207,229,93,200,88,147,193,107,172,383,305,262,254,218,306,164,384,451,110,208,230,94,201,89,148,194,102,173,378,300,263,255,219,307,165,385,450,111,209,231,95,202,84,149,195,103,168,379,301,258,256,220,308,166,386,452,112,204,232,90,203,85,144,117,119,114,115,116,118,669,675,667,674,666,671,644,634,645,638,639,632,640,696,692,687,688,694,690,686,82,423,396,62,391,0,437,226,442,448,182,492,190,510,236,491,503,519,485,83,237,424,398,63,390,2,433,227,443,449,183,493,191,511,481,486,498,520,78,238,425,399,64,392,3,432,222,439,445,184,494,186,512,480,487,499,521,79,239,421,400,65,393,4,434,223,438,444,185,495,187,513,482,488,500,516,80,234,420,401,60,394,5,435,224,440,446,180,496,188,514,483,489,501,517,81,235,422,397,61,395,1,436,225,441,447,181,497,189,515,484,490,502,518,505,507,508,509,504,506,611,606,608,610,609,607,615,613,617,616,612,614,618,624,625,621,622,620,623,619 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#ab7663272fb322647e3a6f8af752cc36283f2dfca26817d870d65fdaf95a91e5, M = {5, 26, 46, 66, 86, 106, 130} 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 22:09:44 · history