Equation 677 Database

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Magma e3d33c10f7a9…

magma e3d33c10f7a9
Size
381
Isomorphism class hash
e3d33c10f7a9c4953d9f5a66c9e365a4b86dae2e3b13623f66d5d7431b57cbc0
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 23:18:32
Display reorder
380,38,310,29,7,22,55,46,14,53,5,39,311,24,8,23,1,56,47,15,48,40,312,25,9,18,0,57,42,16,49,41,313,26,10,19,2,58,43,17,50,36,308,27,11,20,3,59,44,12,51,37,309,28,6,21,4,54,45,13,52,31,33,34,35,30,32,348,349,368,352,351,367,379,378,350,366,115,316,106,74,89,65,113,91,67,82,116,317,107,75,84,83,60,108,92,68,117,314,102,76,85,78,61,109,93,69,118,319,103,77,86,79,62,110,94,70,119,327,104,72,87,80,63,111,95,71,114,315,105,73,88,81,64,112,90,66,98,100,101,96,97,99,353,354,331,334,356,333,330,332,355,375,198,328,189,220,229,205,196,237,213,222,199,321,190,221,230,223,206,197,238,214,200,322,191,216,231,224,207,192,239,215,201,323,186,217,232,225,208,193,234,210,202,320,187,218,233,226,209,194,235,211,203,329,188,219,228,227,204,195,236,212,181,183,184,185,180,182,363,377,374,347,364,373,365,344,346,345,279,306,264,248,263,290,287,255,294,240,280,307,265,249,258,241,291,282,256,295,281,326,266,250,259,242,293,283,257,296,276,300,267,251,260,243,292,284,252,297,277,325,268,246,261,244,288,285,253,298,278,305,269,247,262,245,289,286,254,299,272,274,275,270,271,273,371,342,341,359,376,372,360,361,343,362,145,303,136,177,129,162,153,121,160,169,146,304,137,178,130,170,163,154,122,161,147,324,132,179,131,171,164,155,123,156,148,302,133,174,126,172,165,150,124,157,149,301,134,175,127,173,166,151,125,158,144,318,135,176,128,168,167,152,120,159,138,140,141,142,143,139,358,369,339,370,357,337,338,340,336,335 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#0cf854fe3a8b6e762ec798fbf9e9116be2daa04a71a5b016b186650a7d546e89, 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 23:18:32 · history