Equation 677 Database

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Magma 6880ef46a8cb…

magma 6880ef46a8cb
Size
381
Isomorphism class hash
6880ef46a8cbed1f38e5c6210226946fb639b57d6042c4a89ee7755ffb67975f
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 23:32:17
Display reorder
380,20,19,21,22,23,18,321,322,323,318,319,320,1,0,2,3,4,5,277,282,287,292,297,272,255,260,265,241,246,251,15,16,17,12,13,14,177,152,157,162,167,172,221,225,230,235,211,216,8,9,10,11,6,7,191,198,200,205,181,186,25,24,26,27,28,29,361,347,379,356,366,339,348,336,346,374,53,52,48,49,50,51,309,310,311,306,307,308,41,36,37,38,39,40,276,281,286,291,296,270,256,261,266,240,245,250,47,42,43,44,45,46,176,150,156,161,165,170,220,226,231,236,210,215,63,64,65,60,61,62,192,195,201,206,182,187,57,56,58,59,54,55,363,337,376,357,365,340,349,334,335,371,77,76,72,73,74,75,328,329,324,325,326,327,90,91,92,93,94,95,278,283,288,293,298,273,258,263,268,243,248,253,71,66,67,68,69,70,178,153,158,163,168,173,223,228,233,238,213,218,87,88,89,84,85,86,193,197,203,208,183,188,81,80,82,83,78,79,362,333,375,359,368,342,332,350,343,370,117,116,118,119,114,115,301,300,302,303,304,305,110,111,112,113,108,109,275,280,285,290,295,271,257,262,267,242,247,252,31,32,33,34,35,30,175,151,155,160,166,171,222,227,232,237,212,217,103,104,105,106,107,102,190,196,202,207,180,185,101,100,96,97,98,99,360,353,377,358,367,338,341,352,351,372,148,147,149,144,145,146,312,313,314,315,316,317,132,133,134,135,136,137,279,284,289,294,299,274,259,264,269,244,249,254,139,140,141,142,143,138,179,154,159,164,169,174,224,229,234,239,214,219,129,130,131,126,127,128,194,199,204,209,184,189,123,122,124,125,120,121,364,354,378,355,369,345,344,330,331,373 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#7eadf19d7b6e5946b2d6ebbbf061273ea953f89e2819b4463bfb57d0a1e47218, M = {71} 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 23:32:17 · history