Equation 677 Database

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Magma 08633998030a…

magma 08633998030a
Size
707
Isomorphism class hash
08633998030ac50c55da2ec57120bcff8867278f6d72e0dc31fa9c93421c714f
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 08:51:46
Display reorder
534,536,535,537,538,539,637,128,129,130,131,126,127,89,88,84,85,86,87,103,102,104,105,106,107,8,7,9,10,11,6,279,278,276,280,281,277,261,260,262,263,258,259,319,318,320,321,322,323,148,147,149,144,145,146,157,156,158,159,160,161,135,134,136,137,132,133,359,354,355,356,358,357,53,52,48,49,50,51,456,458,457,459,460,461,494,493,492,496,497,495,470,469,468,471,472,473,481,480,482,484,485,483,432,434,433,435,436,437,447,449,448,444,445,446,527,526,525,522,523,524,517,516,518,521,519,520,617,613,615,616,612,614,633,625,694,663,648,664,685,693,701,698,699,706,700,703,18,19,20,21,22,23,237,236,238,239,234,235,194,193,195,196,197,192,209,208,204,205,206,207,57,56,58,59,54,55,251,250,246,247,248,249,175,174,176,177,178,179,26,25,27,28,29,24,306,311,308,310,307,309,316,315,317,313,312,314,303,302,304,305,300,301,39,38,40,41,36,37,540,542,541,543,544,545,559,558,560,561,562,563,573,575,574,570,572,571,548,547,546,551,549,550,416,415,414,419,417,418,420,422,421,423,424,425,404,403,402,405,406,407,566,565,564,567,568,569,609,608,611,606,610,607,630,618,683,653,654,651,690,673,691,672,680,702,688,692,297,298,299,294,295,296,81,80,82,83,78,79,154,153,155,150,151,152,213,212,214,215,210,211,139,138,140,141,142,143,34,33,35,30,31,32,198,203,199,200,201,202,255,254,256,257,252,253,245,244,240,241,242,243,333,332,334,335,330,331,324,329,325,326,327,328,284,283,285,286,287,282,591,590,593,592,589,588,390,392,391,395,393,394,381,383,382,379,380,378,389,388,387,386,384,385,377,376,375,374,372,373,530,529,528,533,531,532,583,584,582,586,587,585,454,453,455,452,450,451,622,629,621,624,627,628,632,626,668,655,665,657,675,676,682,697,681,704,674,689,43,44,45,46,47,42,341,340,336,337,338,339,183,182,184,185,180,181,231,230,232,233,228,229,0,1,2,3,4,5,221,220,216,217,218,219,227,226,222,223,224,225,186,191,187,188,189,190,14,13,15,16,17,12,293,292,288,289,290,291,349,353,348,350,351,352,347,346,343,342,344,345,368,367,366,371,369,370,365,364,363,360,362,361,429,431,430,427,428,426,601,602,600,603,604,605,596,594,595,599,597,598,555,557,556,552,553,554,581,580,579,577,576,578,409,408,410,413,411,412,619,635,623,620,631,634,643,644,678,670,649,677,666,669,696,687,679,705,695,686,76,77,72,73,74,75,69,68,70,71,66,67,172,171,173,168,169,170,167,166,162,163,164,165,62,61,63,64,65,60,119,118,114,115,116,117,112,111,113,108,109,110,269,268,264,265,266,267,98,97,99,100,101,96,271,270,272,273,274,275,123,122,124,125,120,121,92,91,93,94,95,90,476,475,474,479,477,478,441,443,442,440,438,439,501,503,502,499,500,498,463,462,464,466,467,465,487,486,488,490,491,489,513,515,514,510,511,512,508,507,509,506,504,505,399,401,400,397,398,396,640,641,638,636,639,642,645,646,667,650,647,652,671,659,660,662,656,684,661,658 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#5d364ad3474cdcd7c6d5defafd2fd9bfd394ea971d15e95ed0d16a1c5a75c76d, M = {102, 103, 104, 105, 106, 107, 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 2026-10-06 08:51:48 · history