Equation 677 Database

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Magma a10380f75fbc…

magma a10380f75fbc
Size
381
Isomorphism class hash
a10380f75fbc3888fda76cb463f10e19f7e134da8b2d440c79175e5723eb2e31
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 23:36:16
Display reorder
380,44,159,37,163,27,38,173,157,39,164,326,69,184,62,190,52,327,63,182,189,64,191,75,209,89,215,78,328,90,207,214,91,216,100,234,114,240,103,329,239,232,115,116,241,126,259,139,265,128,324,140,257,141,264,266,1,285,14,290,3,325,289,283,15,16,291,332,372,336,355,333,367,368,337,366,338,26,160,30,165,43,28,167,166,29,170,315,51,186,55,192,68,316,53,193,194,54,197,77,211,81,217,88,317,79,218,219,80,222,102,236,106,242,113,312,244,243,104,105,247,127,261,131,267,138,313,129,268,130,269,272,2,286,6,292,13,314,294,293,4,5,297,335,371,340,357,334,356,365,339,378,347,40,150,31,155,25,41,168,174,42,172,319,65,175,56,180,50,320,66,198,195,67,185,92,200,82,205,76,321,93,223,220,94,210,117,225,107,230,101,322,245,248,118,119,235,142,250,132,255,125,323,143,273,144,270,260,17,275,7,280,0,318,295,298,18,19,281,348,369,341,359,349,373,370,330,358,331,49,161,47,171,46,45,162,156,48,152,306,74,187,72,199,71,307,70,181,188,73,177,99,212,97,224,96,308,95,206,213,98,202,124,237,122,249,121,309,238,231,120,123,227,149,262,147,274,146,310,145,256,148,263,252,24,287,22,299,21,311,288,282,20,23,277,353,379,352,376,354,377,375,350,374,351,35,151,33,158,32,36,153,154,34,169,305,60,176,58,183,57,301,61,179,178,59,196,86,201,84,208,83,300,87,204,203,85,221,111,226,109,233,108,302,228,229,112,110,246,136,251,134,258,133,303,137,254,135,253,271,11,276,9,284,8,304,278,279,12,10,296,344,363,343,361,345,362,360,346,364,342 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#8fb20bcd92e6aa2a90a05ca93478505b73c9a53687ce0472769f23b72ccbb45b, 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 23:36:16 · history