Equation 677 Database

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Magma 7cc38da92899…

magma 7cc38da92899
Size
381
Isomorphism class hash
7cc38da928990aaba44b1a8dcc07bc8fbcaa44abef33a30f309cf3b026fda3a2
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 23:35:55
Display reorder
380,237,232,227,247,252,242,203,207,198,217,222,212,130,120,125,115,106,110,257,262,267,272,277,282,67,73,78,51,56,63,165,170,175,181,186,191,155,160,150,140,145,135,324,325,326,327,328,329,48,38,43,293,6,7,81,295,86,90,95,100,17,287,12,27,32,24,350,370,347,343,332,375,337,356,367,362,236,231,225,246,251,240,201,205,196,216,221,210,131,121,127,117,105,111,255,260,266,271,276,281,65,71,76,53,57,62,168,173,178,183,188,193,156,161,151,141,146,136,312,313,314,315,316,317,46,35,41,290,2,3,80,296,85,91,96,101,16,285,11,25,31,21,351,374,345,340,331,378,335,358,366,360,235,230,226,245,250,241,202,206,197,215,220,211,132,122,126,116,107,112,256,261,265,270,275,280,68,70,75,52,55,60,166,171,176,180,185,190,157,162,152,142,147,137,311,309,310,308,306,307,47,37,42,292,4,5,82,297,87,92,97,102,15,286,10,26,30,22,352,371,346,342,330,376,336,355,368,361,239,234,229,249,254,244,204,209,199,219,224,214,134,124,129,119,109,114,259,264,269,274,279,284,66,72,77,50,58,61,169,174,179,184,189,194,159,164,154,144,149,139,301,300,302,303,304,305,45,36,40,291,0,1,84,299,89,94,99,104,19,289,14,29,34,23,354,373,349,341,334,379,339,359,365,364,238,233,228,248,253,243,200,208,195,218,223,213,133,123,128,118,108,113,258,263,268,273,278,283,69,74,79,54,59,64,167,172,177,182,187,192,158,163,153,143,148,138,320,318,319,323,321,322,49,39,44,294,8,9,83,298,88,93,98,103,18,288,13,28,33,20,353,372,348,344,333,377,338,357,369,363 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#8e237b368ce49904371f47a0bbc192c3f49c4a8da81336b4c06fd9fdc3a5d75d, 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 23:35:56 · history