Equation 677 Database

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Magma f7e29ab36ffa…

magma f7e29ab36ffa
Size
399
Isomorphism class hash
f7e29ab36ffa08a253ae450cde523658e30d15b9e78ea7d19569df0ab57d64af
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 21:31:14
Display reorder
12,13,14,15,16,17,9,10,11,4,5,6,7,8,1,0,2,3,398,95,133,120,96,134,121,97,126,122,98,127,123,90,128,124,91,129,125,92,130,117,93,131,118,94,132,119,104,142,112,105,143,113,106,135,114,107,136,115,99,137,116,100,138,108,101,139,109,102,140,110,103,141,111,156,158,159,160,161,153,154,155,148,149,150,151,152,144,145,146,147,157,389,383,385,397,289,265,315,290,266,316,291,267,317,292,268,318,293,269,319,294,261,320,295,262,321,296,263,322,288,264,323,298,257,307,299,258,308,300,259,309,301,260,310,302,252,311,303,253,312,304,254,313,305,255,314,297,256,306,270,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,271,384,396,395,382,208,247,218,209,248,219,210,249,220,211,250,221,212,251,222,213,243,223,214,244,224,215,245,216,207,246,217,200,239,227,201,240,228,202,241,229,203,242,230,204,234,231,205,235,232,206,236,233,198,237,225,199,238,226,189,191,192,193,194,195,196,197,181,182,183,184,185,186,187,188,180,190,388,390,387,386,177,342,339,178,343,340,179,344,341,171,345,333,172,346,334,173,347,335,174,348,336,175,349,337,176,350,338,169,351,331,170,352,332,162,353,324,163,354,325,164,355,326,165,356,327,166,357,328,167,358,329,168,359,330,373,375,376,377,369,370,371,372,365,366,367,368,360,361,362,363,364,374,392,391,393,394,28,66,37,29,67,38,30,68,39,31,69,40,32,70,41,33,71,42,34,63,43,35,64,44,27,65,36,20,58,46,21,59,47,22,60,48,23,61,49,24,62,50,25,54,51,26,55,52,18,56,53,19,57,45,80,73,74,75,76,77,78,79,89,81,82,83,84,85,86,87,88,72,380,381,379,378 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#e1ee09afca9239b348e61c42ba3dc9e8df04fdf85ef90076d422972a4ab3f69e, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-08 21:31:15 · history