Equation 677 Database

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Magma 6d098f11adaa…

magma 6d098f11adaa
Size
399
Isomorphism class hash
6d098f11adaab7123f5badc60e7719526d1b58cfe646d9f7dc567456316099b0
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
2026-10-07 22:15:03
Display reorder
146,147,148,149,150,151,152,144,145,155,156,157,158,159,160,161,153,154,378,310,169,295,327,328,311,170,296,312,329,162,288,313,330,163,289,314,331,164,290,306,332,165,291,307,324,166,292,325,308,167,293,326,309,168,294,336,178,319,304,337,179,320,305,338,171,321,297,339,172,322,298,340,173,323,299,315,341,174,300,333,175,316,301,334,176,317,302,335,177,318,303,391,385,386,392,273,205,259,6,7,274,206,260,275,8,198,252,276,1,199,253,277,0,200,254,278,2,201,255,270,3,202,256,4,271,203,257,5,272,204,258,15,214,282,268,16,215,283,269,17,207,284,261,9,208,285,262,10,209,286,263,287,11,210,264,12,211,279,265,13,212,280,266,14,213,281,267,383,389,390,384,96,89,219,109,110,97,81,220,98,111,82,221,90,112,83,222,91,113,84,223,92,114,85,224,93,115,86,216,116,94,87,217,108,95,88,218,118,73,105,228,119,74,106,229,120,75,107,230,121,76,99,231,122,77,100,232,101,123,78,233,124,79,102,225,125,80,103,226,117,72,104,227,388,398,397,387,70,189,342,349,351,71,190,344,63,353,191,346,64,354,192,348,65,356,193,350,66,358,194,352,67,343,195,355,345,68,196,357,347,69,197,359,367,182,54,360,369,183,55,362,371,184,56,364,372,185,57,366,374,186,58,368,59,376,187,370,361,188,60,373,363,180,61,375,365,181,62,377,394,395,396,393,35,42,235,131,132,27,43,236,28,133,44,237,29,134,36,238,30,126,37,239,31,127,38,240,32,128,39,241,129,33,40,242,130,34,41,234,140,51,19,244,141,52,20,245,142,53,21,246,143,45,22,247,135,46,23,248,24,136,47,249,137,48,25,250,138,49,26,251,139,50,18,243,382,381,380,379 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#3ff6d35f7ccb6a1ea78521bc0534609f90f460908ad654e7b9929f4cb6316aa6, 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 2026-10-07 22:15:04 · history