Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma eb1b1083ef1f…

magma eb1b1083ef1f
Size
705
Isomorphism class hash
eb1b1083ef1fa9ef9c93d3b74cdc951d46c006979ec1a452c7d1ffb62f79438c
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 16:31:33
Display reorder
660,290,577,589,601,613,288,614,578,590,602,289,612,576,588,600,293,580,616,592,604,291,581,617,593,605,292,579,615,591,603,296,583,619,595,607,294,584,620,596,608,295,582,618,594,606,586,299,622,598,610,599,587,297,623,611,585,298,621,597,609,687,688,686,685,63,340,359,364,382,64,383,341,357,365,65,381,339,358,363,62,336,378,355,360,60,337,379,356,361,61,338,380,354,362,69,346,373,350,370,70,347,374,348,371,71,345,372,349,369,342,68,376,353,366,351,343,66,377,367,344,67,375,352,368,703,704,701,702,134,571,102,270,279,132,280,572,103,271,133,281,570,104,272,137,574,278,105,273,135,575,276,106,274,136,573,277,107,275,140,569,285,100,268,138,567,286,101,269,139,568,287,99,267,565,143,284,96,264,97,566,141,282,265,564,142,283,98,266,671,672,670,669,110,413,421,391,396,108,397,411,422,392,109,398,412,420,390,113,409,399,424,394,111,410,400,425,395,112,408,401,423,393,116,419,402,427,389,114,417,403,428,387,115,418,404,426,388,415,119,405,430,385,431,416,117,406,386,414,118,407,429,384,679,680,678,677,84,208,227,438,448,85,449,209,225,439,86,447,207,226,440,87,204,444,223,441,88,205,445,224,442,89,206,446,222,443,90,214,454,218,436,91,215,455,216,437,92,213,453,217,435,210,93,450,221,432,219,211,94,451,433,212,95,452,220,434,692,691,690,689,249,514,527,532,494,250,492,515,525,533,251,493,513,526,531,248,510,497,523,528,246,511,495,524,529,247,512,496,522,530,240,505,500,518,538,241,506,498,516,539,242,504,499,517,537,508,243,503,521,534,519,509,244,501,535,507,245,502,520,536,699,700,698,697,144,203,161,168,184,145,185,201,159,169,146,183,202,160,170,147,199,180,157,171,148,200,181,158,172,149,198,182,156,173,150,194,190,167,174,151,192,191,165,175,152,193,189,166,176,197,153,186,163,177,164,195,154,187,178,196,155,188,162,179,663,664,662,661,626,15,30,306,41,624,39,16,31,307,625,40,17,32,308,629,14,37,33,309,627,12,38,34,310,628,13,36,35,311,632,21,47,28,304,630,22,45,29,305,631,23,46,27,303,20,635,43,24,300,25,18,633,44,301,19,634,42,26,302,682,683,684,681,253,650,651,648,649,254,652,654,655,653,252,656,658,659,657,256,644,646,647,645,257,637,636,638,639,255,642,640,643,641,259,552,551,562,544,260,553,549,563,545,258,554,550,561,543,555,262,547,558,540,559,556,263,548,541,557,261,546,560,542,695,696,693,694,235,121,462,473,482,236,480,122,463,471,234,481,120,464,472,238,124,485,465,469,239,125,483,466,470,237,123,484,467,468,233,127,488,460,479,231,128,486,461,477,232,126,487,459,478,130,229,491,456,475,457,131,230,489,476,129,228,490,458,474,667,668,665,666,3,319,324,58,78,4,79,320,325,59,5,80,318,326,57,2,322,81,327,54,1,323,82,328,55,0,321,83,329,56,9,317,76,330,49,10,315,77,331,50,11,316,75,332,48,313,8,72,333,52,334,314,6,73,53,312,7,74,335,51,675,676,673,674 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#34f20f8c77c0cbdeb0b8c0e60587a50e7d9ef4f1dbdd588ea7161aafd1a43efd, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 16:31:35 · history