Equation 677 Database

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Magma 0c9b93e7a948…

magma 0c9b93e7a948
Size
381
Isomorphism class hash
0c9b93e7a948adaaf7a1187fe9e22e27a526a023a2ce99ba983df1bf8b8ad3a2
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 23:22:06
Display reorder
380,80,70,61,201,211,222,46,25,36,321,323,319,176,186,191,195,86,95,105,135,116,121,130,146,155,165,241,251,231,255,9,265,270,7,275,8,260,75,65,206,215,41,30,318,320,171,110,100,140,285,151,236,246,5,6,56,225,51,322,181,91,125,160,291,295,281,353,345,335,377,331,374,344,355,368,363,84,74,64,204,214,224,49,29,39,300,303,305,179,189,194,199,89,99,109,139,119,124,134,149,159,169,244,254,234,259,23,269,274,21,279,22,264,79,69,209,219,44,34,304,301,174,114,104,144,289,154,239,249,24,20,59,229,54,302,184,94,129,164,294,299,284,352,349,339,378,334,373,343,358,367,362,82,72,62,202,210,221,47,27,37,313,315,317,177,187,192,197,87,97,107,137,117,122,132,147,157,167,242,252,232,257,13,267,272,11,277,12,262,77,67,207,216,42,32,316,312,172,112,102,142,287,152,237,247,14,10,57,227,52,314,182,92,127,162,292,297,282,350,346,336,375,330,370,342,356,365,361,83,73,63,203,213,223,48,28,38,329,325,327,178,188,193,198,88,98,108,138,118,123,133,148,158,168,243,253,233,258,18,268,273,16,278,17,263,78,68,208,218,43,33,326,328,173,113,103,143,288,153,238,248,19,15,58,228,53,324,183,93,128,163,293,298,283,351,348,338,379,333,372,340,357,366,360,81,71,60,200,212,220,45,26,35,311,307,309,175,185,190,196,85,96,106,136,115,120,131,145,156,166,240,250,230,256,0,266,271,3,276,4,261,76,66,205,217,40,31,308,310,170,111,101,141,286,150,235,245,1,2,55,226,50,306,180,90,126,161,290,296,280,354,347,337,376,332,371,341,359,369,364 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#4422b92082c5ba9f603861f57ee03bc11c9f901f0082cee83e1cd8bfe00bbd4d, M = {70} 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 23:22:07 · history