Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 4e42c47b3e4a…

magma 4e42c47b3e4a
Size
705
Isomorphism class hash
4e42c47b3e4a1d9650e4352dc225c8ebe049565a5c380795e9be04cb0f4962f0
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 21:51:14
Display reorder
660,103,648,651,650,649,611,608,610,104,609,102,628,631,630,629,568,106,571,570,569,588,107,591,590,589,548,105,551,550,549,471,468,470,101,469,431,428,430,99,429,451,448,450,100,449,528,531,530,97,529,488,491,490,98,489,508,511,510,96,509,688,694,690,689,280,644,658,643,645,618,604,603,281,605,279,624,638,623,625,564,276,578,563,565,584,277,598,583,585,544,278,558,543,545,478,464,463,286,465,436,424,423,287,425,458,444,443,285,445,524,538,523,282,525,484,498,483,283,485,504,518,503,284,505,693,701,697,703,266,371,194,189,174,192,369,190,264,175,265,370,193,191,176,367,269,197,188,177,368,267,195,186,178,366,268,196,187,179,200,362,180,272,172,198,360,181,270,173,199,361,182,271,171,365,203,183,275,168,363,201,184,273,169,364,202,185,274,170,664,680,671,661,121,226,311,152,407,309,227,150,122,405,120,225,310,151,406,222,124,307,155,403,223,125,308,153,404,224,123,306,154,402,302,217,147,127,398,300,218,148,128,396,301,216,149,126,397,220,305,146,130,401,221,303,144,131,399,219,304,145,129,400,667,676,678,665,63,653,640,641,652,600,613,601,64,612,65,633,620,621,632,573,62,560,561,572,593,60,581,580,592,553,61,540,541,552,462,473,461,69,472,421,439,437,70,438,440,453,441,71,452,533,521,522,68,532,493,480,482,66,492,513,501,502,67,512,695,686,687,699,0,657,659,642,655,619,617,602,2,615,1,637,639,622,635,577,4,579,562,575,597,5,599,582,595,557,3,559,542,555,479,477,460,7,475,420,435,422,8,433,459,457,442,6,455,537,539,520,10,535,497,499,481,11,495,517,519,500,9,515,704,698,702,691,41,656,646,647,654,606,616,607,39,614,40,636,626,627,634,576,37,566,567,574,596,38,586,587,594,556,36,546,547,554,466,476,467,47,474,426,434,427,45,432,446,456,447,46,454,536,526,527,43,534,496,486,487,44,494,516,506,507,42,514,685,696,700,692,165,252,347,135,419,345,253,136,166,417,167,254,346,137,418,255,164,343,134,415,256,162,344,132,416,257,163,342,133,414,338,258,141,156,410,336,259,142,157,408,337,260,143,158,409,261,341,140,159,413,262,339,138,160,411,263,340,139,161,412,681,684,674,669,109,29,212,323,359,210,27,321,110,357,108,28,211,322,358,25,112,215,319,355,26,113,213,320,356,24,111,214,318,354,207,35,314,115,350,208,33,312,116,348,209,34,313,114,349,31,206,317,118,353,32,204,315,119,351,30,205,316,117,352,666,670,683,675,21,299,237,395,383,238,297,393,22,381,23,298,239,394,382,295,20,236,391,379,296,18,234,392,380,294,19,235,390,378,228,290,386,12,374,229,288,384,13,372,230,289,385,14,373,293,231,389,15,377,291,232,387,16,375,292,233,388,17,376,673,672,663,662,249,53,87,73,335,88,51,74,250,333,251,52,89,72,334,49,248,86,76,331,50,246,84,77,332,48,247,85,75,330,93,59,79,240,326,94,57,80,241,324,95,58,78,242,325,55,92,82,243,329,56,90,83,244,327,54,91,81,245,328,677,668,679,682 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#f6b6fc56ae6a00548325e9d66bb78aa16bb0852529ebdb9883eeafc26b8a7eae, 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 21:51:15 · history