Equation 677 Database

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Magma 58722d89dcaf…

magma 58722d89dcaf
Size
381
Isomorphism class hash
58722d89dcafc2a4f598f365f64d1e870f65beebfc4b026cfda79ceae9562719
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 23:19:32
Display reorder
380,51,46,56,30,35,40,170,175,151,156,161,166,241,246,251,256,260,265,6,7,8,9,10,11,121,126,130,135,140,145,306,311,310,307,308,309,230,235,211,216,221,226,75,80,85,61,65,70,205,181,185,190,195,200,105,110,115,91,96,101,285,281,290,295,271,276,363,332,365,342,351,333,345,358,372,377,50,45,55,31,36,41,171,176,150,155,160,165,240,245,250,255,261,266,1,0,2,3,4,5,120,125,131,136,141,146,321,322,324,326,328,319,231,236,210,215,220,225,76,81,86,60,66,71,206,180,186,191,196,201,106,111,116,90,95,100,286,280,291,296,270,275,360,330,368,337,352,339,346,357,370,375,53,48,58,33,38,43,173,178,153,158,163,168,243,248,253,258,263,268,19,20,21,22,23,18,123,128,133,138,143,148,305,301,300,302,303,304,233,238,213,218,223,228,78,83,88,63,68,73,208,183,188,193,198,203,108,113,118,93,98,103,288,283,293,298,273,278,364,334,366,343,353,340,347,356,371,376,52,47,57,32,37,42,172,177,152,157,162,167,242,247,252,257,262,267,12,13,14,15,16,17,122,127,132,137,142,147,320,323,325,327,329,318,232,237,212,217,222,227,77,82,87,62,67,72,207,182,187,192,197,202,107,112,117,92,97,102,287,282,292,297,272,277,362,341,367,338,354,331,349,359,373,378,54,49,59,34,39,44,174,179,154,159,164,169,244,249,254,259,264,269,27,28,29,24,25,26,124,129,134,139,144,149,312,313,314,315,316,317,234,239,214,219,224,229,79,84,89,64,69,74,209,184,189,194,199,204,109,114,119,94,99,104,289,284,294,299,274,279,361,335,369,344,350,336,348,355,374,379 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#10cca86363523145d0eb290792d3d13154c9d146d7a7475a96ac2cf61ae39af6, M = {75} 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 23:19:38 · history