Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 65983c3af0b6…

magma 65983c3af0b6
Size
705
Isomorphism class hash
65983c3af0b62c0aeb6baf66150213a02a567570858d2483b68795a9e6ff8769
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 16:30:03
Display reorder
660,262,86,348,265,284,260,84,285,346,263,261,85,286,347,264,258,82,283,344,268,259,83,281,345,266,257,81,282,343,267,253,77,275,354,271,75,276,352,251,269,76,277,353,252,270,278,80,350,256,274,279,78,351,254,272,280,79,349,255,273,670,672,662,661,140,31,123,516,372,138,25,370,124,514,139,28,371,125,515,136,18,368,126,512,137,22,369,127,513,135,1,367,128,511,146,48,378,129,522,42,376,130,144,520,45,377,131,145,521,374,36,132,142,518,375,40,133,143,519,373,33,134,141,517,686,685,688,690,166,220,480,384,594,164,218,592,478,382,165,219,593,479,383,162,216,590,476,380,163,217,591,477,381,161,215,589,475,379,157,226,600,486,390,224,598,484,155,388,225,599,485,156,389,596,222,482,160,386,597,223,483,158,387,595,221,481,159,385,671,665,663,666,468,20,546,582,545,466,21,542,541,580,467,4,544,543,581,464,27,537,538,578,465,30,539,540,579,463,24,535,536,577,474,37,557,558,588,39,554,553,472,586,34,555,556,473,587,549,46,550,470,584,551,49,552,471,585,548,43,547,469,583,680,677,683,681,570,7,444,504,290,568,5,291,442,502,569,6,292,443,503,566,10,289,440,500,567,8,287,441,501,565,9,288,439,499,576,13,296,450,510,11,297,448,574,508,12,298,449,575,509,295,16,446,572,506,293,14,447,573,507,294,15,445,571,505,668,669,667,664,205,109,195,408,492,203,110,490,196,406,204,108,491,194,407,208,105,488,191,404,206,106,489,192,405,207,107,487,193,403,211,100,498,201,414,101,496,202,209,412,99,497,200,210,413,494,103,197,214,410,495,104,198,212,411,493,102,199,213,409,698,697,694,693,635,336,633,634,632,627,334,626,624,625,631,335,628,629,630,601,332,562,560,3,602,333,563,561,0,603,331,564,559,2,659,342,657,656,658,340,648,649,651,650,341,653,652,655,654,641,338,640,643,642,645,339,644,647,646,637,337,636,639,638,701,703,704,702,420,97,310,149,303,418,98,301,311,150,419,96,302,312,151,416,93,306,309,152,417,94,304,307,153,415,95,305,308,154,426,88,622,316,623,89,619,317,424,618,87,621,318,425,620,300,91,315,422,147,617,92,313,423,616,299,90,314,421,148,699,695,700,696,609,72,528,246,190,607,73,188,526,247,608,74,189,527,245,605,71,186,524,249,606,69,187,525,250,604,70,185,523,248,615,63,181,534,244,64,179,532,613,242,65,180,533,614,243,184,66,530,611,240,182,67,531,612,241,183,68,529,610,239,673,684,675,679,115,355,396,456,326,116,356,327,394,454,114,357,325,395,455,111,358,329,392,452,112,359,330,393,453,113,360,328,391,451,121,361,324,402,462,362,322,400,122,460,363,323,401,120,461,320,364,398,117,458,321,365,399,118,459,319,366,397,119,457,682,678,676,674,47,60,232,175,432,50,61,430,230,173,44,62,431,231,174,35,59,428,228,178,38,57,429,229,176,41,58,427,227,177,19,51,438,238,170,52,436,236,23,171,53,437,237,17,172,434,54,234,29,169,435,55,235,32,167,433,56,233,26,168,687,691,689,692 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#33fc7ab4b4817466950310b35dd4cd44cb4b00aed5b55945bbae0672c2180aa2, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 16:30:04 · history