Equation 677 Database

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Magma daa3f850ba2d…

magma daa3f850ba2d
Size
381
Isomorphism class hash
daa3f850ba2de982f33edbf8be3a46d0fd8013eb277734d61421cd122099f852
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 23:45:02
Display reorder
380,316,315,317,312,313,314,5,1,0,2,3,4,6,7,8,9,10,11,277,287,297,247,257,267,96,97,98,99,100,101,141,142,143,138,139,140,225,235,185,195,205,215,103,104,105,106,107,102,217,227,237,187,197,207,285,275,134,135,136,295,245,137,255,132,265,133,353,333,352,365,348,375,334,332,363,377,318,323,319,320,321,322,160,161,156,157,158,159,163,164,165,166,167,162,278,288,298,248,258,268,13,14,15,16,17,12,179,174,175,176,177,178,226,236,186,196,206,216,21,22,23,18,19,20,218,228,238,188,198,208,286,276,169,170,171,296,246,172,256,173,266,168,358,355,357,366,336,376,356,335,368,378,305,304,301,300,302,303,40,41,36,37,38,39,43,44,45,46,47,42,270,280,291,240,250,260,126,127,128,129,130,131,85,86,87,88,89,84,224,234,184,194,204,214,125,120,121,122,123,124,211,221,231,180,190,201,284,274,93,94,95,294,244,90,254,91,264,92,346,339,347,361,351,374,340,350,360,370,329,328,324,325,326,327,29,24,25,26,27,28,30,31,32,33,34,35,272,282,292,242,252,262,73,74,75,76,77,72,64,65,60,61,62,63,229,239,189,199,209,219,81,82,83,78,79,80,212,222,232,182,192,202,289,279,71,66,67,299,249,68,259,69,269,70,343,337,344,362,345,379,338,330,367,372,307,306,308,309,310,311,108,109,110,111,112,113,116,117,118,119,114,115,273,283,293,243,253,263,54,55,56,57,58,59,149,144,145,146,147,148,220,230,181,191,200,210,53,48,49,50,51,52,213,223,233,183,193,203,281,271,151,152,153,290,241,154,251,155,261,150,359,349,354,369,342,371,331,341,364,373 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#d9df7de9a291eb9f8afa3ed926081c844b8ee7df4e18920313d7d7d6494810a4, M = {75} 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 23:45:03 · history