Equation 677 Database

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Magma e038449fc419…

magma e038449fc419
Size
381
Isomorphism class hash
e038449fc419ac40f0a6c1d39ddc1eee2cfab04253fe47ba7ab220e560de4a5f
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 23:41:32
Display reorder
380,139,138,140,141,142,143,94,95,90,91,92,93,251,261,271,280,290,241,214,224,234,184,194,204,37,38,39,40,41,36,301,300,302,303,304,305,88,89,84,85,86,87,264,274,284,299,244,254,191,201,211,221,231,180,45,46,47,42,43,44,134,136,137,133,132,135,330,360,345,338,353,346,337,363,372,374,112,111,113,108,109,110,145,146,147,148,149,144,253,263,273,283,293,243,219,229,239,189,199,209,101,96,97,98,99,100,315,316,317,312,313,314,151,152,153,154,155,150,269,279,289,298,249,259,193,203,213,223,233,183,102,103,104,105,106,107,115,117,118,114,119,116,350,362,355,348,349,354,347,368,373,379,74,73,75,76,77,72,31,32,33,34,35,30,256,266,276,286,295,246,218,228,238,188,198,208,48,49,50,51,52,53,309,310,311,306,307,308,24,25,26,27,28,29,268,278,288,297,248,257,196,206,216,226,236,186,58,59,54,55,56,57,78,80,81,83,82,79,344,364,335,340,343,336,339,367,376,378,68,67,69,70,71,66,175,176,177,178,179,174,252,262,272,282,292,242,217,227,237,187,197,207,18,19,20,21,22,23,322,323,318,319,320,321,168,169,170,171,172,173,267,277,287,296,247,258,192,202,212,222,232,182,13,14,15,16,17,12,65,61,62,64,63,60,341,361,358,334,342,359,333,366,370,377,11,10,6,7,8,9,123,124,125,120,121,122,250,260,270,281,291,240,215,225,235,185,195,205,156,157,158,159,160,161,325,326,327,328,329,324,130,131,126,127,128,129,265,275,285,294,245,255,190,200,210,220,230,181,166,167,162,163,164,165,0,3,4,1,5,2,331,369,352,357,332,351,356,365,371,375 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#b66edbbdcc18ab822aeb8c0e517cc0500614bfcd68d760a94b6b8cc01b086dc5, M = {71} 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 23:41:32 · history