Equation 677 Database

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Magma e0f02729028a…

magma e0f02729028a
Size
707
Isomorphism class hash
e0f02729028ac9c9eb0a1f0dd14aad8742e027872cd36c0f2b69fcaef1041216
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 17:53:17
Display reorder
427,426,428,424,425,423,640,269,265,264,267,268,266,256,255,257,252,253,254,131,130,126,127,128,129,221,220,216,217,218,219,230,229,231,232,233,228,307,306,308,309,310,311,339,338,340,341,336,337,273,272,274,275,270,271,281,280,276,277,278,279,244,243,245,240,241,242,359,354,355,356,358,357,95,94,90,91,92,93,453,455,454,458,456,457,414,416,415,411,412,413,531,530,532,529,527,528,467,466,465,468,469,470,478,477,479,480,481,482,491,490,489,493,494,492,363,365,364,361,360,362,403,402,404,405,406,407,607,608,627,626,629,628,630,625,664,683,653,680,668,692,699,698,700,702,705,706,316,312,317,314,315,313,149,148,144,145,146,147,322,321,323,318,319,320,304,303,305,300,301,302,171,170,172,173,168,169,163,162,164,165,166,167,193,192,194,195,196,197,26,25,27,28,29,24,40,39,41,36,37,38,35,34,30,31,32,33,191,190,186,187,188,189,80,79,81,82,83,78,430,429,431,432,433,434,410,409,408,593,594,595,379,378,380,383,381,382,600,599,605,601,602,603,550,549,548,546,547,545,583,582,581,585,586,584,589,588,587,592,590,591,565,564,563,567,568,566,609,606,618,623,619,622,635,634,663,660,675,659,667,674,670,676,694,686,697,704,4,1,5,2,3,0,200,199,201,202,203,198,227,226,222,223,224,225,160,159,161,156,157,158,97,96,98,99,100,101,331,330,332,333,334,335,328,327,329,324,325,326,282,287,283,284,285,286,209,208,204,205,206,207,213,212,214,215,210,211,112,111,113,108,109,110,46,45,47,42,43,44,369,371,370,368,366,367,386,385,384,389,387,388,390,392,391,394,395,393,377,376,375,372,373,374,577,576,575,579,580,578,522,521,523,524,525,526,533,535,534,536,537,538,572,574,573,571,569,570,621,612,631,611,620,632,633,624,651,681,682,677,662,679,678,687,691,685,689,703,16,12,17,14,15,13,295,294,296,297,298,299,103,102,104,105,106,107,236,235,237,238,239,234,288,293,289,290,291,292,181,180,182,183,184,185,8,7,9,10,11,6,89,88,84,85,86,87,69,68,70,71,66,67,153,152,154,155,150,151,176,175,177,178,179,174,23,22,18,19,20,21,498,497,499,500,501,502,512,514,513,509,510,511,506,508,507,504,505,503,495,496,604,596,597,598,518,520,519,517,515,516,562,561,560,558,559,557,542,544,543,539,540,541,552,551,553,554,555,556,615,613,614,610,617,616,644,643,647,690,652,684,655,673,669,693,671,688,696,701,54,61,60,57,55,56,58,63,64,59,65,62,74,73,75,76,77,72,48,53,49,50,51,52,141,140,142,143,138,139,114,119,115,116,117,118,121,120,122,123,124,125,246,251,247,248,249,250,136,135,137,132,133,134,352,351,353,349,348,350,259,258,260,261,262,263,343,347,342,344,345,346,435,437,436,440,438,439,486,488,487,483,484,485,420,422,421,418,419,417,473,472,471,474,475,476,462,464,463,461,459,460,452,451,450,448,449,447,397,396,398,400,401,399,441,443,442,446,444,445,636,638,637,641,642,639,645,646,648,657,649,656,661,665,650,658,654,666,672,695 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#51f9b7d09d33f9fd9b24ec352fcf17309682f23da1a55124c3f963e5739f1055, M = {96, 97, 98, 99, 100, 101, 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 2026-10-07 17:53:18 · history