Equation 677 Database

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Magma 5630af08a59c…

magma 5630af08a59c
Size
399
Isomorphism class hash
5630af08a59c8f91ede2fe0646478d93f276773fdbdcdf8b8ac6e9271a6b89a2
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 20:59:48
Display reorder
306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,381,270,327,305,14,328,271,297,15,272,329,298,16,273,330,299,17,274,331,300,9,275,332,301,10,276,324,302,11,277,325,303,12,278,326,304,13,279,289,336,7,290,337,280,8,291,338,281,1,292,339,282,0,293,340,283,2,294,341,284,3,295,333,285,4,296,334,286,5,288,335,287,6,391,385,386,392,259,108,130,204,109,260,131,205,252,110,132,206,253,111,133,198,254,112,134,199,255,113,126,200,256,114,127,201,257,115,128,202,258,116,129,203,268,139,117,213,140,118,269,214,141,119,261,215,142,120,262,207,143,121,263,208,135,122,264,209,136,123,265,210,137,124,266,211,138,125,267,212,383,389,390,384,95,40,33,146,41,96,34,147,97,42,35,148,98,43,27,149,90,44,28,150,91,36,29,151,92,37,30,152,93,38,31,144,94,39,32,145,104,26,49,155,18,50,105,156,19,51,106,157,20,52,107,158,21,53,99,159,22,45,100,160,23,46,101,161,24,47,102,153,25,48,103,154,388,398,397,387,187,348,244,342,350,188,245,345,180,352,246,347,181,354,247,349,182,357,248,351,183,359,249,353,184,343,250,355,185,344,251,356,186,346,243,358,196,237,366,361,238,368,197,363,239,370,189,365,240,372,190,367,241,375,191,369,242,377,192,371,234,360,193,373,235,362,194,374,236,364,195,376,394,395,396,393,71,74,170,233,75,63,162,225,64,76,163,226,65,77,164,227,66,78,165,228,67,79,166,229,68,80,167,230,69,72,168,231,70,73,169,232,55,179,83,217,171,84,56,218,172,85,57,219,173,86,58,220,174,87,59,221,175,88,60,222,176,89,61,223,177,81,62,224,178,82,54,216,382,379,380,378 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#20b1cce7a1cade189904c93230073395efb2f39f58c55828af81f02ee58e7d7b, 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 20:59:49 · history