Equation 677 Database

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Magma 7dc15d353c48…

magma 7dc15d353c48
Size
381
Isomorphism class hash
7dc15d353c48488d0cf40a38c7904e0b20a52de5bce92362efe2fa4176546c60
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 23:45:42
Display reorder
380,226,221,231,205,211,216,190,195,201,176,181,186,80,86,75,96,280,91,313,314,312,316,317,315,246,235,241,260,250,255,21,265,19,7,10,0,295,156,151,165,170,160,100,105,286,111,115,120,25,30,35,41,270,46,275,51,56,61,66,70,126,290,131,135,140,145,356,350,330,371,360,340,345,365,335,375,225,220,230,206,210,215,191,196,200,175,180,185,81,85,76,95,281,90,318,319,320,321,322,323,247,237,242,262,252,257,20,266,16,5,11,3,296,155,150,166,171,161,101,106,285,110,116,121,27,33,38,40,271,45,276,50,55,60,65,71,125,291,130,136,141,146,355,351,332,370,361,341,346,366,336,376,228,223,233,208,213,218,193,198,203,178,183,188,82,87,77,97,282,92,307,308,306,310,311,309,248,238,243,263,253,258,22,267,15,8,13,2,298,158,153,168,173,163,102,107,287,112,117,122,26,32,37,42,272,47,277,52,57,62,67,72,128,293,133,138,143,148,357,352,333,373,363,342,347,368,337,378,227,222,232,207,212,217,192,197,202,177,182,187,83,88,78,98,283,93,327,328,329,324,325,326,245,236,240,261,251,256,23,268,17,6,12,1,297,157,152,167,172,162,103,108,288,113,118,123,28,31,36,43,273,48,278,53,58,63,68,73,127,292,132,137,142,147,358,353,331,372,362,343,348,367,339,377,229,224,234,209,214,219,194,199,204,179,184,189,84,89,79,99,284,94,301,300,302,303,304,305,249,239,244,264,254,259,24,269,18,9,14,4,299,159,154,169,174,164,104,109,289,114,119,124,29,34,39,44,274,49,279,54,59,64,69,74,129,294,134,139,144,149,359,354,334,374,364,344,349,369,338,379 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#dba6afe67f86b36e533f777300b41b8ae8b2a840d4529c92a6cd7ab996e48d4f, M = {73} 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 23:45:43 · history