Equation 677 Database

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Magma d4fab79122f3…

magma d4fab79122f3
Size
381
Isomorphism class hash
d4fab79122f39b8c877408ccc9990cf2a3f9912303551d73aa034ff13cfe2b75
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:27:15
Display reorder
380,59,152,56,150,58,309,160,159,57,162,52,84,177,81,175,83,310,185,184,82,77,187,109,202,106,200,108,311,210,209,107,102,212,134,227,131,225,133,306,235,234,132,127,237,9,252,6,250,8,2,307,260,259,7,262,34,277,31,275,33,27,308,285,284,32,287,333,334,364,360,359,341,358,340,363,339,60,165,67,155,73,301,167,169,70,172,63,86,190,91,180,98,300,192,194,94,88,198,111,215,116,205,123,302,217,220,119,113,222,136,240,141,230,148,303,242,245,144,138,247,10,265,16,255,23,13,304,267,270,19,272,35,290,41,280,47,38,305,291,295,44,297,346,336,366,368,374,344,373,353,377,349,53,157,54,158,50,325,161,154,51,151,55,78,182,79,183,75,326,186,179,76,80,176,103,207,104,208,100,327,211,204,101,105,201,128,232,129,233,125,328,236,229,126,130,226,3,257,4,258,0,5,329,261,254,1,251,28,282,29,283,25,30,324,286,279,26,276,338,337,355,357,362,331,361,332,356,330,62,164,66,156,72,321,168,170,69,174,65,87,189,92,181,97,322,193,195,95,90,199,112,214,117,206,122,323,218,219,120,115,224,137,238,142,231,147,318,243,244,145,140,249,12,263,17,256,22,15,319,268,269,20,274,37,289,42,281,48,40,320,293,294,45,299,348,342,367,370,375,343,371,352,378,351,61,163,68,153,74,317,166,171,71,173,64,85,188,93,178,99,312,191,196,96,89,197,110,213,118,203,124,313,216,221,121,114,223,135,239,143,228,149,314,241,246,146,139,248,11,264,18,253,24,14,315,266,271,21,273,36,288,43,278,49,39,316,292,296,46,298,347,335,365,369,376,345,372,354,379,350 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#5288d0d523845c575da229f12df029472a44afa32b43c22de9e2c374ed83e9c4, M = {66} 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 23:27:15 · history