Equation 677 Database

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Magma a7ed56f8b158…

magma a7ed56f8b158
Size
705
Isomorphism class hash
a7ed56f8b158af5319eafa9c9f99d79371761959a960d7defacff36239cb825e
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 21:24:06
Display reorder
660,545,553,63,548,558,565,573,64,568,578,585,593,65,588,598,613,62,608,618,605,633,625,60,628,638,653,645,61,648,658,508,69,505,513,518,70,525,533,528,538,71,485,493,488,498,423,68,428,425,429,444,66,452,447,456,464,67,472,467,476,691,686,699,688,555,556,100,546,551,575,576,101,566,571,595,596,99,586,591,616,96,606,611,615,636,635,97,626,631,656,655,98,646,651,506,106,515,516,511,107,535,536,526,531,105,495,496,486,491,434,102,435,424,426,453,103,454,445,450,473,104,474,465,470,702,696,690,693,230,254,14,273,318,228,252,12,274,319,229,253,13,275,320,257,17,272,321,233,255,231,15,270,322,256,232,16,271,323,264,20,236,260,316,18,234,258,265,317,19,235,259,266,315,239,23,263,267,312,237,21,261,268,313,238,22,262,269,314,667,675,664,681,200,171,154,378,402,198,172,155,379,403,199,173,153,380,404,170,150,381,405,203,168,201,151,382,406,169,202,152,383,407,376,145,195,177,400,146,196,178,377,401,144,197,179,375,399,194,148,176,372,396,192,149,174,373,397,193,147,175,374,398,682,662,678,674,541,540,114,549,550,561,560,115,569,570,581,580,116,589,590,600,117,609,610,601,621,620,118,629,630,641,640,119,649,650,509,112,500,501,510,113,520,521,529,530,111,481,480,489,490,420,108,421,432,433,441,109,440,448,449,461,110,460,468,469,704,700,689,692,559,542,122,547,557,579,562,120,567,577,599,582,121,587,597,602,125,607,617,619,622,639,123,627,637,642,659,124,647,657,507,128,519,502,517,126,539,522,527,537,127,499,482,487,497,437,131,430,431,436,457,129,442,446,455,477,130,462,466,475,685,701,698,703,554,544,189,552,543,574,564,190,572,563,594,584,191,592,583,604,188,612,603,614,624,634,186,632,623,644,654,187,652,643,512,180,514,504,503,181,534,524,532,523,182,494,484,492,483,438,183,439,427,422,459,184,458,451,443,478,185,479,471,463,695,687,697,694,303,366,90,342,354,304,367,91,343,355,305,368,92,344,356,369,93,345,357,302,370,300,94,346,358,371,301,95,347,359,340,88,309,364,352,89,310,365,341,353,87,311,363,339,351,308,84,360,336,348,306,85,361,337,349,307,86,362,338,350,673,677,670,666,282,163,32,141,58,283,164,30,142,59,284,162,31,143,57,166,35,140,54,285,167,286,33,138,55,165,287,34,139,56,132,27,280,161,49,28,281,159,133,50,29,279,160,134,48,276,26,157,135,52,277,24,158,136,53,278,25,156,137,51,684,661,668,679,1,206,248,225,390,0,204,246,226,391,2,205,247,227,392,209,251,224,393,3,207,4,249,222,394,208,5,250,223,395,216,243,6,212,388,244,7,210,217,389,245,8,211,218,387,9,242,215,219,384,10,240,213,220,385,11,241,214,221,386,671,683,676,669,414,294,47,330,80,415,295,45,331,78,416,296,46,332,79,297,43,333,83,417,298,418,44,334,81,299,419,42,335,82,328,38,412,292,75,36,413,293,329,76,37,411,291,327,77,408,41,288,324,74,409,39,289,325,72,410,40,290,326,73,663,680,672,665 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#ef4a4f27352a122a7b1088a6208971ffd57fb3858716fe27bd37fbc92d64744c, 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 21:24:09 · history