Equation 677 Database

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Magma 9382873f083c…

magma 9382873f083c
Size
707
Isomorphism class hash
9382873f083c52ad6599cfce4313534a4adb4ff3f0589f1d4558ee7b2fb5bda5
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 09:23:36
Display reorder
353,352,351,348,349,350,644,51,47,48,49,50,46,184,183,185,186,181,182,206,205,207,208,209,210,173,172,174,169,170,171,126,125,127,128,129,124,180,179,175,176,177,178,290,307,245,268,300,267,308,272,292,284,278,279,296,259,1,0,2,3,216,215,217,218,219,220,119,118,120,121,122,123,382,381,383,378,379,380,577,576,578,579,580,581,501,500,502,498,499,497,466,465,464,463,461,462,470,472,471,468,469,467,343,342,344,347,345,346,582,583,584,587,585,586,485,487,486,489,490,488,377,376,375,373,374,372,624,625,612,637,635,633,632,636,634,688,685,657,670,700,704,705,703,698,706,696,309,283,276,277,273,291,298,263,231,232,233,234,155,154,156,260,304,287,295,261,211,212,213,214,28,33,29,30,31,32,79,78,80,81,76,77,25,24,26,27,22,23,223,222,224,225,226,221,112,117,113,114,115,116,99,98,94,95,96,97,111,110,106,107,108,109,460,459,458,456,457,455,453,452,454,449,450,451,542,544,543,539,540,541,441,440,442,438,439,437,337,336,338,341,339,340,529,528,527,530,531,532,421,420,419,422,423,424,414,413,415,418,416,417,402,401,403,404,405,406,613,640,606,608,614,615,628,627,611,667,697,659,656,677,686,693,690,668,687,680,132,134,135,130,131,133,53,52,54,55,56,57,36,35,37,38,39,34,42,41,43,44,45,40,11,10,12,13,14,15,189,188,190,191,192,187,266,289,299,244,265,306,280,285,281,274,310,293,303,271,254,255,256,257,246,247,248,249,250,251,198,197,193,194,195,196,391,390,392,393,394,395,597,596,595,598,599,594,479,481,480,482,483,484,369,371,370,366,367,368,335,334,333,331,330,332,494,496,495,492,493,491,478,477,476,473,474,475,603,605,604,600,602,601,572,571,570,574,575,573,638,639,641,623,620,619,607,621,626,678,699,661,660,684,694,695,675,674,683,673,101,103,104,105,100,102,264,243,305,288,241,242,297,262,227,228,229,230,253,252,269,301,270,302,294,311,286,282,258,275,90,89,91,92,93,88,87,86,82,83,84,85,200,199,201,202,203,204,168,167,163,164,165,166,159,158,160,161,162,157,238,237,239,240,236,235,362,361,360,364,365,363,400,399,563,396,397,398,386,385,384,389,387,388,412,411,410,409,407,408,428,430,429,426,427,425,588,591,590,593,592,589,549,548,550,547,545,546,538,537,536,533,534,535,444,443,445,446,447,448,618,610,616,617,631,609,622,630,629,702,689,655,682,676,692,701,679,681,691,669,21,17,18,19,20,16,65,64,66,67,68,69,314,312,315,316,317,313,320,318,321,322,323,319,8,7,9,4,5,6,141,140,136,137,138,139,148,153,149,150,151,152,143,142,144,145,146,147,70,75,71,72,73,74,329,328,325,324,326,327,63,62,58,59,60,61,432,431,433,434,435,436,552,551,553,554,555,556,558,557,559,561,562,560,520,519,518,517,515,516,521,523,522,525,526,524,356,355,354,357,358,359,568,567,569,566,564,565,505,504,503,506,507,508,512,514,513,511,509,510,642,651,643,648,647,645,650,646,649,663,672,652,653,664,665,671,662,658,666,654 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#967d317cf04778fc566aed88226f2ec73cf112a27da243deb50eb6f078cd5ea3, M = {108, 109, 110, 111, 112, 113, 132} 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 09:23:37 · history