Equation 677 Database

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Magma 4566475943d4…

magma 4566475943d4
Size
707
Isomorphism class hash
4566475943d46af7781a820308d6dc853c83cfefeb932f5cb1b383fc3ab912d2
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
2026-10-06 08:19:22
Display reorder
524,526,525,521,522,523,640,241,240,242,243,244,245,251,246,247,248,249,250,88,87,89,84,85,86,98,97,99,100,101,96,134,133,135,136,137,132,45,44,46,47,42,43,37,36,38,39,40,41,8,7,9,10,11,6,224,223,225,226,227,222,238,239,235,237,236,234,317,316,313,312,314,315,343,342,344,347,345,346,444,443,442,440,441,439,408,407,406,405,403,404,380,379,378,381,382,383,333,335,334,331,330,332,433,435,434,436,437,438,480,479,478,481,484,540,559,558,557,555,556,554,560,562,561,537,538,536,606,611,616,608,617,607,637,645,647,697,670,678,700,679,701,696,686,702,705,706,24,29,25,26,27,28,32,33,34,35,30,31,49,48,50,51,52,53,229,228,230,231,232,233,64,63,65,60,61,62,13,12,14,15,16,17,19,18,20,21,22,23,286,285,287,282,283,284,281,280,276,277,278,279,178,177,179,174,175,176,129,128,130,131,126,127,409,411,410,413,414,412,592,591,593,589,588,590,350,349,348,353,351,352,365,364,363,360,361,362,415,417,416,418,419,420,494,496,495,491,492,493,503,505,504,507,508,506,497,499,498,502,500,501,359,358,357,356,354,355,629,624,638,639,649,648,641,635,642,681,676,691,683,664,674,673,665,682,688,698,81,80,82,83,78,79,202,203,198,199,200,201,197,196,192,193,194,195,160,159,161,156,157,158,256,255,257,252,253,254,120,125,121,122,123,124,292,291,293,289,288,290,1,5,0,2,3,4,209,208,204,205,206,207,187,186,188,189,190,191,168,173,169,170,171,172,391,390,389,392,393,394,489,488,490,485,486,487,400,399,398,397,395,396,464,463,462,465,466,467,542,461,460,459,457,458,575,574,573,572,570,571,600,601,602,605,603,604,552,551,553,548,549,550,472,471,473,469,470,468,614,646,628,644,618,630,636,643,633,689,680,692,690,660,671,684,662,687,677,699,215,214,210,211,212,213,265,266,267,268,269,264,272,271,273,274,275,270,306,311,307,308,309,310,113,112,108,109,110,111,300,301,302,303,304,305,261,260,262,263,258,259,104,103,105,106,107,102,149,148,144,145,146,147,154,153,155,150,151,152,295,299,294,296,297,298,581,580,579,577,576,578,422,421,423,424,425,426,567,569,568,565,564,566,427,429,428,431,432,430,586,585,584,583,582,587,370,369,371,367,368,366,513,512,514,511,509,510,372,374,373,377,375,376,597,595,599,598,594,596,631,627,615,632,625,626,634,651,650,704,668,675,703,661,669,685,663,693,694,695,57,56,58,59,54,55,180,181,182,183,184,185,167,166,162,163,164,165,217,216,218,219,220,221,326,328,327,324,325,329,67,66,68,69,70,71,92,91,93,94,95,90,318,319,320,321,322,323,77,76,72,73,74,75,140,139,141,142,143,138,119,118,114,115,116,117,532,531,530,533,534,535,384,386,385,388,387,483,516,515,517,519,520,518,401,402,539,529,527,528,547,546,545,563,543,544,450,449,448,447,445,446,456,455,454,451,452,453,541,474,475,476,477,482,338,337,336,341,339,340,623,622,620,613,610,609,619,621,612,672,656,657,667,654,652,655,653,658,659,666 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#33d45c5563bf4abb244f69cfa51749fb5a869f311e4fb00d8e6c25812252a226, M = {72, 73, 74, 75, 76, 77, 126} 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 2026-10-06 08:19:23 · history