Equation 677 Database

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Magma f400d38bbcd6…

magma f400d38bbcd6
Size
381
Isomorphism class hash
f400d38bbcd60bd6d2ef7976ae8d18b7f0f1d7ae2f7e07675fbfb658bf6ec732
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:33:32
Display reorder
380,81,80,82,83,78,79,73,74,75,76,77,72,109,110,111,112,113,108,328,329,324,325,326,327,283,298,223,238,253,268,249,264,279,294,219,234,159,174,187,204,129,142,119,114,115,116,117,118,260,275,290,215,230,245,191,208,133,146,163,178,193,170,200,125,138,155,348,363,378,360,342,349,355,370,374,343,11,10,6,7,8,9,0,2,3,4,5,1,58,59,54,55,56,57,306,307,308,309,310,311,281,296,221,236,251,266,247,262,277,292,217,232,157,172,185,202,127,140,48,49,50,51,52,53,265,280,295,220,235,250,189,206,131,144,161,176,188,175,205,130,143,160,338,356,376,362,331,339,361,375,372,332,69,68,70,71,66,67,61,62,63,64,65,60,44,45,46,47,42,43,305,301,300,302,303,304,284,299,224,239,254,269,243,258,273,288,213,228,153,168,183,198,123,136,39,40,41,36,37,38,259,274,289,214,229,244,192,209,134,147,164,179,184,169,199,124,137,154,337,359,379,364,340,336,357,369,368,341,26,25,27,28,29,24,34,35,30,31,32,33,104,105,106,107,102,103,318,319,320,321,322,323,282,297,222,237,252,267,246,261,276,291,216,231,156,171,194,201,126,139,99,100,101,96,97,98,257,272,287,212,227,242,190,207,132,145,162,177,182,167,197,122,149,152,347,350,377,358,335,346,353,367,371,330,88,87,89,84,85,86,92,93,94,95,90,91,18,19,20,21,22,23,316,317,312,313,314,315,278,293,218,233,248,263,241,256,271,286,210,226,151,166,181,196,120,148,17,12,13,14,15,16,255,270,285,211,225,240,186,203,128,141,158,173,180,165,195,121,135,150,333,352,373,354,345,334,351,366,365,344 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#83cf1f35d4fb7256f5d65d48e163e6c0239fd3c4b75a82ae41fd7ea0fe92a1c5, M = {76} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:33:33 · history