Equation 677 Database

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Magma e8efe61d1d46…

magma e8efe61d1d46
Size
381
Isomorphism class hash
e8efe61d1d460c290913520a832402d73095dce88c2f74a7cd7e76ff70195387
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 23:21:22
Display reorder
380,125,140,133,162,161,312,154,126,169,147,120,141,134,163,156,148,313,155,127,170,121,142,135,164,157,149,314,150,128,171,122,143,136,165,158,144,315,151,129,172,123,138,137,166,159,145,316,152,130,173,146,139,124,132,167,160,317,153,131,168,175,177,178,179,174,176,370,355,357,371,372,338,339,353,356,354,39,54,53,18,17,302,10,46,25,3,40,55,48,19,12,4,303,11,47,26,41,56,49,20,13,5,304,6,42,27,36,57,50,21,14,1,305,7,43,28,37,58,51,22,15,0,301,8,44,29,2,59,38,52,23,16,300,9,45,24,31,33,34,35,30,32,336,352,368,334,351,350,335,337,333,369,225,182,239,204,203,306,196,232,211,189,226,183,234,205,198,190,307,197,233,212,227,184,235,206,199,191,311,192,228,213,222,185,236,207,200,186,310,193,229,214,223,180,237,208,201,187,308,194,230,215,188,181,224,238,209,202,309,195,231,210,217,219,220,221,216,218,358,360,364,374,342,341,377,373,340,359,106,63,114,85,78,321,77,113,92,70,107,64,115,86,79,71,323,72,108,93,102,65,116,87,80,66,325,73,109,94,103,60,117,88,81,67,327,74,110,95,104,61,118,89,82,68,329,75,111,90,69,62,105,119,84,83,318,76,112,91,98,100,101,96,97,99,375,376,362,361,343,378,344,363,365,379,249,267,259,293,285,324,277,257,295,275,250,268,260,288,286,270,326,278,252,296,251,269,261,289,287,271,328,279,253,297,246,264,262,290,282,272,319,280,254,298,247,265,263,291,283,273,320,281,255,299,274,266,248,258,292,284,322,276,256,294,242,243,240,244,241,245,347,348,346,367,332,331,345,330,349,366 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#3e111b62f9a34338b05a1eef31634eeac98395a3f63ae47135fffb9f3d1d128d, 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 23:21:24 · history