Equation 677 Database

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Magma 7f49712a42c3…

magma 7f49712a42c3
Size
705
Isomorphism class hash
7f49712a42c35f4e0ddcf7870d39edd1079c2a6cc2ffb9df8c7e348285002e14
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 19:43:49
Display reorder
660,608,611,33,613,609,628,631,34,633,629,648,651,35,653,649,591,588,32,593,589,551,548,30,553,549,568,571,31,573,569,24,431,428,433,429,25,451,448,453,449,26,471,468,473,469,491,27,488,493,489,511,28,508,513,509,531,29,528,533,529,685,692,687,696,614,600,267,607,612,634,621,268,627,632,654,641,269,647,652,580,594,266,587,592,540,554,264,547,552,574,560,265,567,572,273,424,434,427,432,274,440,454,447,452,275,460,474,467,472,481,272,494,487,492,500,270,514,507,512,520,271,534,527,532,695,701,693,699,321,357,105,285,393,322,358,106,286,394,323,359,107,287,395,356,320,104,284,392,354,318,102,282,390,319,355,103,283,391,96,348,312,276,384,97,349,313,277,385,98,350,314,278,386,351,99,315,279,387,352,100,316,280,388,353,101,317,281,389,668,674,678,664,229,261,145,345,417,230,262,146,346,418,228,263,144,347,419,260,232,148,344,416,258,233,149,342,414,231,259,147,343,415,151,252,235,336,408,152,253,236,337,409,150,254,234,338,410,255,154,238,339,411,256,155,239,340,412,257,153,237,341,413,681,662,683,671,610,619,90,605,606,630,639,91,625,626,650,659,92,645,646,599,590,93,585,586,559,550,94,545,546,570,579,95,565,566,88,439,430,425,426,89,459,450,445,446,87,479,470,465,466,499,84,490,485,486,519,85,510,505,506,539,86,530,525,526,689,690,697,703,603,602,13,616,604,623,622,14,636,624,643,642,16,656,644,582,583,19,596,584,542,543,21,556,544,563,562,23,576,564,12,438,420,422,421,15,442,443,456,444,17,462,463,476,464,482,18,483,496,484,502,20,503,516,504,522,22,523,536,524,694,691,702,700,615,618,11,617,601,635,638,9,637,620,655,658,10,657,640,598,595,7,597,581,558,555,8,557,541,575,578,6,577,561,2,437,435,436,423,1,458,455,457,441,0,478,475,477,461,498,5,495,497,480,518,3,515,517,501,538,4,535,537,521,698,704,686,688,297,240,156,75,369,298,241,157,76,370,299,242,158,77,371,243,296,159,74,368,244,294,160,72,366,295,245,161,73,367,162,246,288,81,360,163,247,289,82,361,164,248,290,83,362,249,165,291,80,363,250,166,292,78,364,251,167,293,79,365,665,672,675,661,114,58,120,71,140,115,59,121,69,138,116,57,122,70,139,54,117,123,67,143,55,118,124,68,141,119,56,125,66,142,126,49,112,62,135,127,50,113,60,136,128,48,111,61,137,52,129,108,65,134,53,130,109,63,132,51,131,110,64,133,680,682,670,667,333,381,225,46,405,334,382,226,47,406,335,383,227,45,407,380,332,224,42,404,378,330,222,43,402,331,379,223,44,403,216,372,324,37,396,217,373,325,38,397,218,374,326,36,398,375,219,327,40,399,376,220,328,41,400,377,221,329,39,401,669,677,679,684,195,172,188,309,208,196,173,186,310,209,197,171,187,311,207,168,194,191,308,204,169,192,189,306,205,193,170,190,307,206,183,178,201,300,214,184,179,202,301,215,185,177,203,302,213,174,182,200,303,210,175,180,198,304,211,176,181,199,305,212,676,663,673,666 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#a687d51fdba056b88b615f4c33c4bd51079879725771af3a621b4a64ac93acf2, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 19:43:50 · history