Equation 677 Database

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Magma e9811bbc64f8…

magma e9811bbc64f8
Size
381
Isomorphism class hash
e9811bbc64f806ae54e2602991b4272aba85062cb7c470fa8104fb69c00bf06d
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 23:43:37
Display reorder
380,276,227,250,324,187,6,162,72,97,137,326,197,1,222,157,289,67,245,107,132,147,17,57,82,172,327,212,260,237,122,152,22,62,87,177,328,201,265,242,112,47,37,42,32,27,192,102,77,167,281,217,292,325,255,127,142,12,52,92,182,329,206,272,233,117,297,352,332,347,357,337,377,340,367,362,372,278,228,253,321,188,7,163,73,98,138,323,198,3,223,158,287,68,248,108,133,148,18,58,83,173,318,213,263,239,123,153,23,63,88,178,319,203,268,243,113,48,38,43,33,28,193,103,78,168,283,218,293,322,258,128,143,13,53,93,183,320,208,273,234,118,298,353,333,348,358,338,378,343,368,363,373,275,226,251,304,185,9,161,70,95,135,303,195,0,221,156,285,65,246,106,130,146,16,56,80,171,300,210,262,235,120,150,21,61,85,176,302,200,267,240,111,46,36,41,31,25,190,101,75,165,280,216,290,305,256,126,141,11,50,90,181,301,205,271,232,116,295,350,331,346,355,335,376,341,366,361,371,279,229,254,306,189,8,164,74,99,139,308,199,4,224,159,288,69,249,109,134,149,19,59,84,174,309,214,264,236,124,154,24,64,89,179,310,204,269,244,114,49,39,44,34,29,194,104,79,169,284,219,294,307,259,129,144,14,54,94,184,311,209,274,231,119,299,354,334,349,359,339,379,344,369,364,374,277,225,252,315,186,5,160,71,96,136,317,196,2,220,155,286,66,247,105,131,145,15,55,81,170,312,211,261,238,121,151,20,60,86,175,313,202,266,241,110,45,35,40,30,26,191,100,76,166,282,215,291,316,257,125,140,10,51,91,180,314,207,270,230,115,296,351,330,345,356,336,375,342,365,360,370 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#ccc40d3a7572bc817f1e0e643b0b882fca97901472beda34cd022d7e757b2855, 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 23:43:38 · history