Equation 677 Database

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Magma b06c088bde03…

magma b06c088bde03
Size
381
Isomorphism class hash
b06c088bde03ddd69ac071fe515003d4f315081a8a16b38fb38e6b475849eb00
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 23:34:16
Display reorder
380,124,166,159,328,174,146,152,139,131,132,133,125,167,160,319,175,147,153,140,126,134,120,162,161,321,176,148,154,141,127,135,121,163,156,323,177,149,155,142,128,122,136,164,157,324,178,144,150,143,129,165,137,123,158,326,179,145,151,138,130,172,168,169,170,171,173,358,373,371,341,342,360,359,361,362,372,29,36,35,320,50,22,57,15,0,8,9,24,37,30,322,51,23,58,16,2,10,25,38,31,325,52,18,59,17,3,11,26,39,32,327,53,19,54,12,4,27,6,40,33,329,48,20,55,13,5,41,7,28,34,318,49,21,56,14,1,42,44,45,46,47,43,367,330,347,349,334,333,332,368,348,331,104,62,84,301,76,97,83,90,111,118,119,105,63,85,300,77,98,78,91,112,114,106,64,86,302,72,99,79,92,113,115,107,65,87,303,73,100,80,93,108,102,116,60,88,304,74,101,81,94,109,61,117,103,89,305,75,96,82,95,110,68,70,71,66,67,69,363,374,344,345,379,376,343,365,375,364,280,254,247,315,268,273,240,296,286,288,289,281,255,248,312,269,274,241,297,287,290,276,256,249,317,264,275,242,298,282,291,277,257,250,316,265,270,243,299,283,278,292,252,251,313,266,271,244,294,284,253,293,279,246,314,267,272,245,295,285,260,262,263,258,259,261,356,355,340,377,346,353,357,378,366,354,194,236,229,307,221,187,222,180,201,208,209,195,237,230,308,216,188,223,181,202,204,196,238,231,309,217,189,224,182,203,205,197,239,232,310,218,190,225,183,198,192,206,234,233,311,219,191,226,184,199,235,207,193,228,306,220,186,227,185,200,213,215,210,211,212,214,350,369,336,339,352,337,351,370,338,335 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#889f5984d564a0102d69c2441a9759c96b931b04e9110bc017112fc402619ea4, 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 23:34:17 · history