Equation 677 Database

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Magma 45a8b97c2ffb…

magma 45a8b97c2ffb
Size
705
Isomorphism class hash
45a8b97c2ffbf3e3c977027ef7472b6f8edf8c2427d7e5735328d480e06d6015
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 21:52:55
Display reorder
704,223,150,246,214,224,151,215,247,222,152,213,248,226,153,249,210,227,154,250,211,225,155,212,251,148,221,244,205,149,219,206,245,220,147,204,243,217,144,240,208,145,218,209,241,146,216,207,242,233,231,232,229,230,228,239,237,234,235,236,238,675,673,674,672,525,128,499,512,526,126,510,500,527,127,511,498,524,131,502,515,522,129,503,513,523,130,514,501,123,516,497,507,124,517,508,495,518,125,509,496,519,122,493,506,120,520,504,494,121,521,505,492,483,484,485,482,480,481,489,490,487,488,486,491,664,666,665,667,30,162,262,22,31,163,23,263,32,164,21,261,33,165,258,18,34,166,259,19,35,167,20,260,160,28,253,13,161,29,14,254,27,159,12,252,24,156,256,16,157,25,17,257,158,26,15,255,648,649,650,651,652,653,654,655,658,656,657,659,686,684,685,687,82,105,54,68,83,106,66,55,81,107,67,56,78,104,57,71,79,102,58,69,80,103,70,59,96,73,52,63,97,74,64,53,72,98,65,51,76,99,48,62,100,77,60,49,101,75,61,50,85,86,84,88,89,87,91,92,93,94,95,90,701,703,700,702,610,570,635,647,611,571,645,633,609,572,646,634,606,573,631,643,607,574,632,644,608,575,642,630,568,601,626,638,569,602,636,624,600,567,637,625,604,564,629,641,565,605,639,627,566,603,640,628,612,613,614,615,616,617,618,619,623,621,622,620,691,690,689,688,300,184,324,293,301,185,291,325,302,183,292,326,303,180,327,289,304,181,328,290,305,182,288,329,190,306,330,299,191,307,297,331,308,189,298,332,309,186,333,295,187,310,296,334,188,311,294,335,320,318,319,323,321,322,315,316,313,314,312,317,662,661,663,660,389,4,411,425,387,5,423,412,388,3,424,413,385,1,410,421,386,0,408,422,384,2,420,409,10,395,417,431,11,393,429,418,394,9,430,419,391,6,416,427,7,392,428,414,8,390,426,415,406,407,405,402,403,404,397,398,399,400,401,396,694,693,695,692,269,172,46,576,267,173,577,47,268,171,578,45,265,168,42,579,266,169,43,580,264,170,581,44,178,275,37,582,179,273,583,38,274,177,584,36,271,174,40,585,175,272,586,41,176,270,587,39,287,285,286,283,284,282,278,276,280,281,279,277,682,683,681,680,456,143,435,447,457,141,448,436,458,142,449,437,459,139,434,446,460,140,432,444,461,138,445,433,134,462,441,453,132,463,454,442,464,133,455,443,465,137,440,452,135,466,450,438,136,467,451,439,474,475,476,477,478,479,472,473,470,468,469,471,696,698,699,697,539,113,561,595,537,111,596,562,538,112,594,563,535,109,560,598,536,110,558,599,534,108,597,559,119,530,552,593,117,528,591,553,529,118,592,554,533,115,555,589,116,531,590,556,114,532,588,557,541,542,540,544,545,543,547,548,549,550,551,546,671,668,670,669,365,199,336,349,363,200,350,337,364,198,348,338,361,202,339,352,362,203,340,353,360,201,351,341,197,371,342,355,195,369,356,343,370,196,354,344,367,193,345,358,194,368,359,346,192,366,357,347,381,382,383,380,378,379,372,373,377,375,376,374,676,678,677,679 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#f8838644c69f7fdfa74529bfff2a78ed4214bd0b4502e0a1aafa31f9fac0d26b, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 21:52:55 · history