Equation 677 Database

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Magma 4f84f2471109…

magma 4f84f2471109
Size
381
Isomorphism class hash
4f84f247110941690a2139b675dbaeab02669bc0fffcf2523dc3c0b931a06627
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 23:35:52
Display reorder
380,157,152,298,167,172,162,196,200,191,180,185,176,127,132,137,142,292,147,328,329,327,325,326,324,47,52,57,37,272,42,92,282,87,102,107,97,24,28,32,265,11,16,211,216,206,225,231,220,115,122,110,5,287,4,237,240,245,252,257,262,277,77,82,72,62,67,332,362,367,357,371,336,347,352,342,375,158,153,297,168,173,163,198,203,193,183,188,178,128,133,138,143,293,148,320,318,319,323,321,322,48,53,58,38,273,43,93,283,88,103,108,98,22,26,31,268,13,18,213,218,208,228,233,223,118,123,113,6,288,7,238,243,248,253,258,263,278,78,83,73,63,68,333,363,368,358,373,337,348,353,343,378,155,150,296,165,171,160,195,201,190,181,186,175,126,131,136,140,291,145,312,313,314,315,316,317,45,50,56,36,270,41,90,281,85,100,105,96,21,25,30,267,12,17,210,215,205,226,230,221,117,120,112,3,285,2,235,241,246,250,255,260,276,76,80,70,61,65,330,361,366,355,370,335,345,351,340,376,156,151,295,166,170,161,197,202,192,182,187,177,125,130,135,141,290,146,308,306,307,311,309,310,46,51,55,35,271,40,91,280,86,101,106,95,20,27,33,266,10,15,212,217,207,227,232,222,116,121,111,0,286,1,236,242,247,251,256,261,275,75,81,71,60,66,331,360,365,356,372,339,346,350,341,377,159,154,299,169,174,164,199,204,194,184,189,179,129,134,139,144,294,149,305,303,304,302,301,300,49,54,59,39,274,44,94,284,89,104,109,99,23,29,34,269,14,19,214,219,209,229,234,224,119,124,114,8,289,9,239,244,249,254,259,264,279,79,84,74,64,69,334,364,369,359,374,338,349,354,344,379 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#8e237b368ce49904371f47a0bbc192c3f49c4a8da81336b4c06fd9fdc3a5d75d, M = {70} 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 23:35:53 · history