Equation 677 Database

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Magma 1ba8c454516e…

magma 1ba8c454516e
Size
707
Isomorphism class hash
1ba8c454516ec48bb3238b342ccefbe131b90cd5d2d4cb671f910b72016ee2f7
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 03:27:23
Display reorder
417,419,418,420,421,422,626,218,217,219,220,221,216,96,97,98,99,100,101,144,149,145,146,147,148,79,78,80,81,82,83,118,117,119,114,115,116,208,207,209,204,205,206,54,59,55,56,57,58,236,235,237,238,239,234,246,251,247,248,249,250,72,77,73,74,75,76,309,308,310,311,306,307,448,447,449,452,450,451,566,568,567,569,570,571,556,555,554,558,559,557,443,442,441,446,444,445,343,342,344,341,339,340,541,540,539,538,536,537,473,472,471,474,475,572,596,598,597,595,593,594,574,573,575,577,591,576,614,606,615,612,608,643,624,645,647,696,667,675,699,677,701,700,690,703,706,705,1,5,0,2,3,4,10,11,6,7,8,9,70,69,71,66,67,68,240,245,241,242,243,244,37,36,38,39,40,41,65,64,60,61,62,63,288,293,289,290,291,292,294,299,295,296,297,298,287,286,282,283,284,285,178,177,179,174,175,176,214,213,215,210,211,212,431,430,429,432,433,434,544,543,542,547,545,546,579,580,578,583,581,582,438,440,439,435,436,437,529,528,527,524,525,526,391,390,392,388,389,387,381,383,382,385,386,384,552,551,553,548,549,550,481,480,479,478,476,477,637,629,610,635,649,648,627,642,628,683,680,695,676,660,673,674,666,681,689,697,181,180,182,183,184,185,186,187,188,189,190,191,102,107,103,104,105,106,272,271,273,274,275,270,134,133,135,136,137,132,276,281,277,278,279,280,141,140,142,143,138,139,45,44,46,47,42,43,90,95,91,92,93,94,264,269,265,266,267,268,254,253,255,256,257,252,366,368,367,364,365,363,377,376,375,380,378,379,427,426,428,423,424,425,484,483,482,487,485,486,503,505,504,501,502,500,605,604,603,602,600,601,506,508,507,510,511,509,488,490,489,493,491,492,561,560,562,564,565,563,621,646,622,644,609,607,625,623,611,693,682,691,694,661,669,678,657,692,685,698,29,28,24,25,26,27,12,13,14,15,16,17,155,154,150,151,152,153,305,304,301,300,302,303,49,48,50,51,52,53,313,312,314,315,316,317,260,259,261,262,263,258,192,197,193,194,195,196,158,157,159,160,161,156,170,169,171,172,173,168,35,34,30,31,32,33,373,372,374,371,369,370,405,407,406,408,409,410,413,412,411,415,416,414,399,401,400,402,403,404,334,333,335,332,331,330,520,519,518,523,521,522,398,397,396,393,394,395,497,499,498,496,494,495,531,530,532,534,535,533,631,613,638,634,630,636,632,651,650,702,670,684,704,659,668,679,658,686,688,687,222,223,224,225,226,227,203,198,199,200,201,202,162,167,163,164,165,166,20,19,21,22,23,18,326,328,327,324,325,329,230,231,229,232,233,228,129,128,130,131,126,127,321,320,322,323,319,318,113,112,108,109,110,111,125,124,120,121,122,123,84,89,85,86,87,88,517,516,515,512,513,514,348,350,349,345,346,347,586,588,587,599,584,585,462,464,463,459,460,461,337,336,338,590,589,592,470,469,468,467,465,466,361,360,362,359,357,358,353,352,351,355,356,354,453,455,454,456,457,458,617,618,619,639,633,620,641,640,616,665,656,662,671,652,653,655,654,663,664,672 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 = {102, 103, 104, 105, 106, 107, 129} 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 03:27:24 · history