Equation 677 Database

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Magma e38a378f2db4…

magma e38a378f2db4
Size
381
Isomorphism class hash
e38a378f2db4f99fd4cd6434d62c04aa45ee268f5084d41cc44e1b3df47fdb40
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 23:49:34
Display reorder
380,62,72,67,57,277,52,177,182,187,192,197,202,167,172,162,297,157,152,208,213,218,222,227,232,147,137,142,132,292,127,47,42,272,39,27,34,97,87,92,82,282,77,5,266,2,17,22,12,243,248,238,258,263,253,107,102,287,115,121,112,300,301,302,303,304,305,362,357,367,372,352,342,332,336,347,377,61,70,65,56,275,51,175,181,186,190,195,201,165,171,160,296,156,150,205,211,216,221,226,231,146,135,140,131,290,126,46,41,270,38,26,32,95,85,90,81,280,76,9,267,0,15,20,10,241,246,236,257,262,252,106,101,285,116,122,111,313,312,314,315,316,317,360,355,366,371,350,340,331,335,345,375,63,73,68,58,278,53,178,183,188,193,198,203,168,173,163,298,158,153,207,212,217,223,228,233,148,138,143,133,293,128,48,43,273,35,28,31,98,88,93,83,283,78,7,268,3,18,23,11,242,247,237,255,260,251,108,103,288,118,123,113,320,319,318,322,323,321,363,358,368,373,353,343,333,337,348,378,64,74,69,59,279,54,179,184,189,194,199,204,169,174,164,299,159,154,209,214,219,224,229,234,149,139,144,134,294,129,49,44,274,36,29,30,99,89,94,84,284,79,8,269,4,19,24,14,244,249,239,259,264,254,109,104,289,119,124,114,307,306,308,309,310,311,364,359,369,374,354,344,334,338,349,379,60,71,66,55,276,50,176,180,185,191,196,200,166,170,161,295,155,151,206,210,215,220,225,230,145,136,141,130,291,125,45,40,271,37,25,33,96,86,91,80,281,75,6,265,1,16,21,13,240,245,235,256,261,250,105,100,286,117,120,110,326,325,324,328,329,327,361,356,365,370,351,341,330,339,346,376 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 = {69} 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 23:49:35 · history