Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma c3e57686adb5…

magma c3e57686adb5
Size
705
Isomorphism class hash
c3e57686adb5f2a3a28927bd3a23e374b5e44dd4ce0c5c9d48eb16a38b737f6d
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 15:17:10
Display reorder
660,296,594,586,585,595,554,294,546,545,555,566,574,565,575,295,646,299,654,645,655,297,606,614,605,615,298,626,634,625,635,486,494,291,485,495,506,514,292,505,515,526,534,293,525,535,465,474,466,290,475,429,426,288,436,437,454,446,289,445,455,700,696,693,694,118,582,580,598,599,542,119,541,559,558,560,562,578,579,117,641,114,642,658,659,115,600,602,619,618,116,621,622,638,639,480,482,109,499,498,500,502,110,519,518,521,522,108,538,539,478,462,460,112,479,424,423,113,439,438,442,440,111,458,459,685,701,695,692,94,368,177,160,154,366,95,178,161,155,179,367,159,153,93,176,90,371,156,150,91,174,369,157,151,92,175,370,158,152,168,363,85,166,145,169,364,86,167,146,170,365,84,165,144,162,362,171,88,148,360,172,89,163,149,361,173,87,164,147,684,683,673,678,218,64,416,247,30,65,216,414,248,31,415,63,246,32,217,419,221,60,250,33,219,417,61,251,34,220,418,62,249,35,411,70,224,245,28,412,71,222,243,29,413,69,223,244,27,241,66,410,227,24,67,408,225,242,25,68,409,226,240,26,677,675,663,682,141,583,592,597,584,543,142,552,557,544,572,563,577,564,143,652,140,643,657,644,138,612,603,617,604,139,632,623,637,624,492,483,132,497,484,512,503,133,517,504,532,523,134,537,524,477,463,472,135,464,432,435,136,431,425,443,452,137,457,444,697,699,691,689,17,587,588,593,596,547,15,548,553,556,568,567,573,576,16,648,13,647,653,656,14,608,607,613,616,12,628,627,633,636,488,487,23,493,496,508,507,21,513,516,528,527,22,533,536,473,467,468,19,476,433,434,20,428,430,447,448,18,453,456,688,690,686,698,232,590,581,589,591,550,233,540,549,551,561,570,569,571,231,640,228,650,649,651,229,601,610,609,611,230,620,630,629,631,481,490,238,489,491,501,510,239,509,511,520,530,237,529,531,469,470,461,234,471,427,422,235,420,421,450,441,236,449,451,702,687,703,704,98,57,123,261,7,58,96,124,262,8,125,59,263,6,97,122,101,56,260,10,99,120,54,258,11,100,121,55,259,9,129,48,104,252,5,130,49,102,253,3,131,50,103,254,4,255,51,128,107,0,52,126,105,256,2,53,127,106,257,1,661,671,670,681,282,308,320,206,356,306,283,318,204,354,319,307,205,355,284,323,285,311,209,359,286,321,309,207,357,287,322,310,208,358,315,303,280,212,351,316,304,281,210,352,317,305,279,211,353,215,302,314,276,350,300,312,277,213,348,301,313,278,214,349,665,672,666,667,180,380,76,404,43,378,181,77,402,44,75,379,403,42,182,72,183,383,407,46,184,73,381,405,47,185,74,382,406,45,82,375,186,399,41,83,376,187,400,39,81,377,188,401,40,398,374,78,189,37,372,79,190,396,38,373,80,191,397,36,680,674,676,662,197,344,392,272,332,342,195,390,270,330,391,343,271,331,196,395,193,347,275,335,194,393,345,273,333,192,394,346,274,334,387,339,203,267,327,388,340,201,268,328,389,341,202,269,329,266,338,386,199,326,336,384,200,264,324,337,385,198,265,325,664,668,669,679 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#101de34e785e3f92e4e627a1da3ddc1fe7ebde0c6c88cd6039e0733ba8ec0ae0, 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 15:17:11 · history