Equation 677 Database

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Magma 01629e21ba2c…

magma 01629e21ba2c
Size
381
Isomorphism class hash
01629e21ba2c5f11d7425ff8d77b86c92ae7acdf645abdb798c46bacf3a43e7f
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 23:51:27
Display reorder
380,199,185,231,218,327,205,186,238,225,192,200,180,193,232,219,329,206,187,239,226,181,201,194,233,220,319,207,188,234,227,182,202,195,228,221,321,208,189,235,222,203,183,196,229,216,323,209,190,236,223,197,184,198,230,217,325,204,191,237,224,211,213,214,215,210,212,353,351,369,370,335,334,352,349,354,350,267,260,246,299,306,284,252,245,291,275,268,261,270,250,294,307,285,253,240,292,262,269,271,249,295,308,286,254,241,293,263,264,272,251,296,309,287,255,242,288,265,258,273,247,297,310,282,256,243,289,274,259,266,248,298,311,283,257,244,290,281,277,278,279,280,276,357,371,339,358,356,337,338,336,372,355,85,79,66,118,302,105,72,65,111,92,86,80,93,67,119,303,106,73,60,112,81,87,94,68,114,304,107,74,61,113,82,88,95,69,115,305,102,75,62,108,89,83,90,70,116,301,103,76,63,109,91,78,84,71,117,300,104,77,64,110,97,99,100,101,96,98,360,361,373,340,341,378,375,344,359,374,158,152,139,126,315,178,145,132,125,165,159,153,166,140,127,316,179,146,133,120,154,160,167,141,128,317,174,147,134,121,155,161,162,142,129,312,175,148,135,122,156,150,163,143,130,313,176,149,136,123,164,151,157,138,131,314,177,144,137,124,170,172,173,168,169,171,376,366,362,343,377,342,363,364,379,365,47,27,14,0,322,53,34,21,8,40,42,28,41,15,2,324,48,35,22,9,29,43,36,16,3,326,49,30,23,10,24,44,37,17,4,328,50,31,18,11,45,25,38,12,5,318,51,32,19,6,39,26,46,13,1,320,52,33,20,7,59,55,56,57,58,54,346,345,367,333,331,348,330,347,368,332 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#fdfa89915be5d31f2386e8b8ea269a0304e33f3ecc732e692a9cd354624a419e, M = {66} 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 23:51:28 · history