Equation 677 Database

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Magma ca5eb05de039…

magma ca5eb05de039
Size
707
Isomorphism class hash
ca5eb05de039105b0f9ad1c061bb76ae56ad398a881ed3ef1da7c321819fa705
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
2026-10-08 17:47:02
Display reorder
320,319,321,322,323,318,704,208,204,209,206,207,205,307,311,306,308,309,310,326,325,327,328,329,324,220,219,221,216,217,218,125,130,126,127,128,129,26,25,27,28,29,24,315,314,316,317,312,313,0,1,2,3,4,5,278,277,279,280,281,276,228,231,232,233,230,229,332,331,330,333,334,335,474,473,475,478,476,477,482,484,483,481,479,480,364,363,362,360,361,359,395,397,396,400,398,399,459,458,460,457,455,456,430,429,428,427,425,426,401,403,402,404,405,406,564,566,565,568,569,567,579,581,580,578,577,576,623,624,626,609,608,625,638,627,640,684,683,662,682,703,702,690,695,701,706,705,36,38,37,40,35,39,42,41,43,44,45,46,96,95,97,98,99,100,87,86,88,83,84,85,71,76,72,73,74,75,66,65,67,68,69,70,300,305,301,302,303,304,155,160,156,157,158,159,287,286,282,283,284,285,146,148,145,143,144,147,154,153,149,150,151,152,374,376,375,372,373,371,492,491,493,494,495,496,342,497,343,344,345,346,355,354,353,357,358,356,352,351,350,347,348,349,525,527,526,522,523,524,520,519,521,517,518,516,435,434,436,433,431,432,448,447,446,444,445,443,630,631,629,632,633,628,637,634,612,660,692,671,661,697,679,667,676,680,688,698,141,137,142,139,140,138,261,260,262,263,258,259,115,114,116,117,118,113,184,183,179,180,181,182,265,264,266,267,268,269,57,56,58,53,54,55,94,93,89,90,91,92,62,61,63,64,59,60,52,51,47,48,49,50,78,80,77,81,82,79,199,198,200,201,202,203,536,535,534,537,538,539,582,583,584,585,586,587,379,378,377,381,382,380,338,336,337,340,341,339,388,387,386,383,384,385,575,574,573,572,570,571,540,542,541,543,544,545,553,552,554,557,555,556,438,437,439,440,441,442,613,611,622,607,621,606,636,635,641,672,694,668,669,693,675,678,663,689,673,699,253,255,254,257,252,256,169,168,170,171,172,167,239,238,234,235,236,237,291,290,292,293,288,289,294,299,295,296,297,298,240,245,241,242,243,244,275,274,270,271,272,273,176,175,177,178,173,174,103,102,104,105,106,101,250,246,249,247,248,251,110,109,111,112,107,108,599,598,597,595,594,596,515,514,513,511,512,510,593,592,591,588,590,589,604,601,600,605,602,603,413,415,414,417,418,416,505,504,506,508,509,507,502,501,503,499,500,498,411,410,412,409,407,408,423,422,424,419,420,421,646,642,644,639,610,643,645,648,647,696,685,666,691,700,677,674,665,686,681,687,192,194,193,196,197,195,9,8,10,11,6,7,17,16,12,13,14,15,21,20,22,23,18,19,210,215,211,212,213,214,166,165,161,162,163,164,119,124,120,121,122,123,30,34,191,31,32,33,222,227,223,224,225,226,190,186,189,187,188,185,131,136,132,133,134,135,449,451,450,453,454,452,389,391,390,394,392,393,549,551,550,548,546,547,365,367,366,370,368,369,463,462,461,464,465,466,528,530,529,531,532,533,486,485,487,489,490,488,560,558,559,561,562,563,471,470,472,467,468,469,620,619,617,618,615,616,614,650,649,656,664,651,655,670,654,653,652,657,658,659 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#10d95f4d62da29d597cabb26c5d7a2889acb76e08f2897cdd164594c6bfbc5c4, M = {60, 61, 62, 63, 64, 65, 145} 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 2026-10-08 17:47:04 · history