Equation 677 Database

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Magma 6c05aeca0bb6…

magma 6c05aeca0bb6
Size
381
Isomorphism class hash
6c05aeca0bb6c5a748f2a47d9e0a511090bd80819b34b998e9926d7188ac6d7b
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 23:21:19
Display reorder
380,183,189,305,38,56,54,36,184,306,190,55,37,321,191,185,41,322,204,198,53,39,320,205,199,51,40,206,326,200,52,30,202,196,208,48,31,203,197,209,49,32,201,195,207,50,187,45,193,33,181,188,46,194,34,182,186,47,192,35,180,43,44,57,58,59,42,371,346,374,345,373,372,370,349,348,347,256,262,327,105,93,94,106,257,318,263,95,107,329,261,255,108,300,247,271,90,109,319,248,272,91,110,246,310,270,92,100,245,269,251,118,101,243,267,249,119,99,244,268,250,117,260,115,266,103,254,258,116,264,104,252,259,114,265,102,253,113,111,97,98,96,112,368,343,366,342,365,369,367,341,340,344,232,238,315,84,72,73,85,233,313,239,74,86,314,237,231,87,316,223,217,69,88,317,224,218,70,89,222,328,216,71,79,221,215,227,67,80,219,213,225,68,78,220,214,226,66,236,64,242,82,230,234,65,240,83,228,235,63,241,81,229,62,60,76,77,75,61,359,334,357,333,355,356,358,332,330,331,171,177,308,29,17,15,27,172,309,178,16,28,325,179,173,2,324,162,156,14,1,307,163,157,12,0,164,323,158,13,21,160,154,166,9,22,161,155,167,10,23,159,153,165,11,175,6,150,24,169,176,7,152,25,170,174,8,151,26,168,4,5,18,19,20,3,378,353,376,352,375,379,377,351,350,354,299,281,301,130,134,135,131,297,311,279,133,129,312,280,298,132,303,212,294,121,136,304,210,295,122,137,211,302,296,120,149,273,290,285,123,147,274,288,286,124,148,275,289,287,125,276,146,282,128,291,277,144,283,126,292,278,145,284,127,293,139,140,143,141,142,138,362,337,360,336,364,363,361,335,339,338 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#361cd7d31899a45dc6b82eab400f4c3e28bcaf437570d13d99e5c6d74a965946, 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 23:21:20 · history