Equation 677 Database

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Magma fa30946ea4e0…

magma fa30946ea4e0
Size
381
Isomorphism class hash
fa30946ea4e0412165520db5e3d9d23a7cbafea54b96670225967f19d5249c39
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 23:49:47
Display reorder
380,252,247,242,260,265,255,187,192,182,202,207,197,71,60,65,56,280,51,35,40,46,275,26,31,287,96,92,81,86,75,152,157,162,167,172,177,321,322,323,318,319,320,115,121,110,100,105,291,237,227,232,222,212,217,125,135,130,295,141,145,20,19,10,1,6,270,350,360,345,335,340,372,367,356,330,377,253,248,243,263,268,258,188,193,183,203,208,198,73,63,68,58,283,53,38,43,48,278,28,33,288,98,93,83,88,78,153,158,163,168,173,178,315,316,317,312,313,314,118,123,113,103,108,293,238,228,233,223,213,218,128,138,133,298,143,148,23,17,13,3,8,273,353,363,348,338,343,373,369,358,333,378,251,246,240,261,266,256,186,191,181,200,206,195,70,61,66,55,281,50,36,41,45,276,25,30,286,97,91,80,85,76,150,155,160,166,171,175,327,328,329,324,325,326,116,120,111,101,106,290,236,226,231,220,210,215,126,136,131,296,140,146,22,15,12,2,7,272,351,361,346,337,341,371,366,355,331,375,254,249,244,264,269,259,189,194,184,204,209,199,74,64,69,59,284,54,39,44,49,279,29,34,289,99,94,84,89,79,154,159,164,169,174,179,300,302,301,304,305,303,119,124,114,104,109,294,239,229,234,224,214,219,129,139,134,299,144,149,24,18,14,4,9,274,354,364,349,339,344,374,368,359,334,379,250,245,241,262,267,257,185,190,180,201,205,196,72,62,67,57,282,52,37,42,47,277,27,32,285,95,90,82,87,77,151,156,161,165,170,176,311,309,310,308,306,307,117,122,112,102,107,292,235,225,230,221,211,216,127,137,132,297,142,147,21,16,11,0,5,271,352,362,347,336,342,370,365,357,332,376 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#edf00a573dad398077d9e9a7f74ac5f2ae5601c41b127cdfd29539dca9f6b98a, 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 23:49:48 · history