Equation 677 Database

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Magma ce7d3a6875c8…

magma ce7d3a6875c8
Size
595
Isomorphism class hash
ce7d3a6875c8c5115f202dd091636073946393ae8ba90c3273b8937921edaa9b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 17:30:50
Display reorder
278,276,277,279,280,281,274,273,275,272,271,270,328,327,329,330,325,326,320,319,321,322,323,324,318,317,313,314,315,316,555,556,592,593,594,168,169,170,171,172,173,177,179,178,174,176,175,134,133,132,135,136,137,257,259,258,261,262,260,125,124,123,121,122,120,238,237,239,234,235,236,128,127,126,130,131,129,109,108,110,113,111,112,116,115,114,118,119,117,466,465,467,468,463,464,443,442,444,439,440,441,471,470,472,473,474,469,475,480,476,477,478,479,453,452,454,455,456,451,457,462,458,459,460,461,446,445,447,448,449,450,551,512,520,519,525,536,545,540,530,568,557,566,572,582,578,587,144,146,145,149,147,148,185,184,183,180,181,182,140,139,138,141,142,143,263,265,264,267,268,266,189,191,190,188,186,187,211,212,210,215,213,214,151,150,152,153,154,155,157,156,158,161,159,160,164,163,162,166,167,165,483,482,484,485,486,481,497,496,498,493,494,495,504,503,499,500,501,502,487,492,488,489,490,491,284,282,285,286,287,288,283,506,509,507,508,505,292,291,293,294,289,290,552,513,517,518,527,537,547,541,531,567,558,563,574,583,579,589,34,33,35,30,31,32,50,49,48,51,52,53,47,46,45,42,43,44,250,249,248,245,246,247,56,55,54,58,59,57,228,230,229,233,231,232,41,40,39,37,38,36,63,65,64,61,62,60,70,69,71,66,67,68,400,399,401,402,397,398,412,411,413,414,409,410,405,404,406,407,408,403,394,393,395,396,391,392,381,380,382,383,384,379,385,390,386,387,388,389,374,373,375,376,377,378,553,514,515,516,528,535,548,543,533,570,560,564,575,585,580,590,93,95,94,92,90,91,204,205,206,209,207,208,106,105,107,104,102,103,254,256,255,252,253,251,73,72,74,75,76,77,218,217,216,220,221,219,100,99,101,96,97,98,82,81,83,80,78,79,89,88,87,85,86,84,420,419,415,416,417,418,432,431,427,428,429,430,425,424,426,421,422,423,436,435,437,438,433,434,301,306,302,303,304,305,312,311,307,308,309,310,300,299,295,296,297,298,554,511,524,523,529,539,549,544,534,571,561,565,576,586,581,591,192,193,194,195,196,197,203,202,201,199,198,200,2,0,1,3,4,5,243,244,269,240,242,241,29,28,27,25,26,24,225,227,226,224,222,223,8,7,6,10,11,9,15,17,16,13,14,12,22,21,23,18,19,20,364,363,365,366,361,362,342,341,337,338,339,340,369,368,370,371,372,367,331,336,332,333,334,335,349,354,350,351,352,353,359,358,360,355,356,357,348,347,343,344,345,346,550,510,522,521,526,538,546,542,532,569,559,562,573,584,577,588 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#f04ca8125d7ce546c7552606527b36663a07f654279810fba8dfdb3271b338ee, M = the submagma generated by {30, 60} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-08 17:30:51 · history